Quadratic Functions — Test Answers

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What is the rate of change for the interval between 0 and 2 for the quadratic equation f of x is equal to 2 x squared plus x minus 3 represented in the table?

1 fifth

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Which equation, when graphed, has x -intercepts at 2 comma 0 and 4 comma 0 and a y -intercept of 0 comma negative 16 ?

f of x is equal to negative open paren x plus 2 close paren times open paren x plus 4 close paren

f of x is equal to negative open paren x minus 2 close paren times open paren x minus 4 close paren

f of x is equal to negative 2 open paren x minus 2 close paren open paren x minus 4 close paren

f of x is equal to negative 2 open paren x plus 2 close paren open paren x plus 4 close paren

Which is one of the transformations applied to the graph of f of x is equal to x squared to change it into the graph of g of x is equal to 4 x squared plus 24 x plus 30 ?

The graph of f of x is equal to x squared is shifted up 30 units.

The graph of f of x is equal to x squared is widened.

The graph of f of x is equal to x squared is reflected over the x -axis.

The graph of f of x is equal to x squared is shifted left 3 units.

Which is the graph of f of x is equal to x squared minus 2 x plus 3 ?

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately negative 1 comma 3. The curve extends symmetrically upward, with the left arm rising steeply into the upper-left portion of the plane and the right arm visible near the y-axis in the upper-center area of the plane.

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately negative 3 comma 2. The curve extends symmetrically upward, with the left arm rising steeply into the upper-left portion of the plane and the right arm visible in the upper-center area near the y-axis.

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately 0 comma 3, on the y-axis. The curve extends symmetrically upward, with the left arm rising into the upper-left area of the plane and the right arm ending near the point 1 comma 5 at the upper-right edge of the visible portion of the curve.

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately 2 comma 0, on the x-axis. The curve extends symmetrically upward to the left and to the right, with the left arm rising into the upper-left portion of the plane and the right arm rising into the upper-right portion of the plane.

Which function has an axis of symmetry of x is equal to negative 2 ?

f of x is equal to x negative 2 squared negative 1

f of x is equal to x plus 2 squared negative 1

f of x is equal to x plus 1 squared negative 2

f of x is equal to x negative 1 squared plus 2

What is the vertex of the graph of the function f of x is equal to x squared plus 8 x minus 2 ?

negative 4 comma negative 18

negative 4 comma 18

negative 8 comma negative 2

0 comma negative 2

The function f of x is equal to negative open paren x minus 3 close paren squared plus 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x What is the maximum area of the rectangle?

6 square units

3 square units

9 square units

12 square units

Which function in vertex form is equivalent to f of x is equal to x squared plus x plus 1 ?

f of x is equal to open paren x plus 1 fourth close paren squared plus 5 fourths

f of x is equal to open paren x plus 1 half close paren squared plus 3 fourths

f of x is equal to open paren x plus 1 fourth close paren squared plus 3 fourths

f of x is equal to open paren x plus 1 half close paren squared plus 5 fourths

The axis of symmetry for a function in the form f of x is equal to x squared plus 4 x minus 5 is x is equal to negative 2 What are the coordinates of the vertex of the graph?

negative 2 comma negative 9

negative 9 comma negative 2

negative 17 comma negative 2

negative 2 comma negative 17

Which point is an x -intercept of the quadratic function f of x is equal to open paren x minus 8 close paren times open paren x plus 9 close paren ?

negative 9 comma 0

0 comma negative 8

9 comma 0

0 comma 8

Which graph represents the function f of x is equal to negative x squared plus 5 ?

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. A downward-opening parabola is plotted that passes through the point negative 3 comma negative 4, has a vertex at the point 0 comma 5, and passes through the point 3 comma negative 4.

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. A downward-opening parabola is plotted that passes through the point negative 6 comma negative 9, has a vertex at the point negative 5 comma 0, and passes through the point negative 2 comma negative 9.

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. An upward-opening parabola is plotted that passes through the point negative 2 comma 9, has a vertex at the point 0 comma 5, and passes through the point 2 comma 9.

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. An upward-opening parabola is plotted that passes through the point negative 8 comma 9, has a vertex at the point negative 5 comma 0, and passes through the point negative 2 comma 10.

What is the axis of symmetry for the function f of x is equal to 7 minus 4 x plus x squared ?

x is equal to 3

x is equal to negative 3

x is equal to 2

x is equal to negative 2

Given the function f of x is equal to negative 5 x squared minus x plus 20 , find f of 3

negative 13

negative 28

Which is one of the transformations applied to the graph of f of x is equal to x squared to change it into the graph of g of x is equal to negative x squared plus 16 x minus 44 ?

The graph of f of x is equal to x squared is widened.

The graph of f of x is equal to x squared is shifted left 8 units.

The graph of f of x is equal to x squared is shifted down 44 units.

The graph of f of x is equal to x squared is reflected over the x -axis.

The function f of x is equal to negative x squared minus 2 x plus 15 is shown on the graph. What are the domain and range of the function?

The domain is all real numbers. The range is start set y such that y is less than 16 end set .

The domain is start set x such that negative 5 is less than or equal to x comma x is less than or equal to 3 end set . The range is start set y such that y is less than or equal to 16 end set .

The domain is start set x such that negative 5 is less than x comma x is less than 3 end set . The range is start set y such that y is less than 16 end set .

The domain is all real numbers. The range is start set y such that y is less than or equal to 16 end set .

What is the range of the function?

all real numbers greater than or equal to negative 3

all real numbers greater than or equal to 4

all real numbers less than or equal to negative 3

all real numbers less than or equal to 4

What is the function written in vertex form?

f of x is equal to 4 times open paren x plus 6 close paren squared plus 154

f of x is equal to 4 times open paren x plus 6 close paren squared plus 10

f of x is equal to 4 times open paren x plus 6 close paren squared minus 134

f of x is equal to 4 times open paren x plus 6 close paren squared minus 26

What is the function written in vertex form?

f of x is equal to 5 times open paren x plus 4 close paren minus 80

f of x is equal to 5 times open paren x plus 8 close paren minus 80

f of x is equal to 5 times open paren x plus 4 close paren squared minus 80

f of x is equal to 5 times open paren x plus 8 close paren squared minus 80

Which function could be represented by the graph on the coordinate plane?

f of x is equal to x plus 8 squared negative 6

f of x is equal to x plus 8 squared plus 6

f of x is equal to x negative 8 squared minus 6

f of x is equal to x negative 8 squared plus 6

What is the equation of the translated function, g of x , if f of x is equal to x squared ?

g of x is equal to x minus 5 squared plus 2

g of x is equal to x minus 2 squared plus 5

g of x is equal to x plus 5 squared plus 2

g of x is equal to x plus 2 squared plus 5

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Quadratic Functions — Test Answers

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