What is f(x) = x2 – 8x + 11 written in vertex form?
Sample Response: A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
x2 + 8x + [___]
16
671314
21324354
x + 3x + 9x + 12x + 36
What is h(x) = 7 + 10x + x2 written in vertex form?
Determine the vertex form of g(x) = x2 + 2x – 1. Which graph represents g(x)?
Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
What is true about the function h(x) = x2 + 20x – 17? Check all that apply. The vertex of h is (–10, –117).The vertex form of the function is h(x) = (x + 20)2 – 17.The maximum value of the function is –17. To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units.The axis of symmetry of function h is x = 20.
The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function?
Explain the steps necessary to convert a quadratic function in standard form to vertex form.
To convert a quadratic function from standard form to vertex form, you use the process of completing the square. First, focus on the first two terms (the x^2 and x terms). Create a perfect square trinomial by adding a zero pair. The value of this pair is found by taking half of the coefficient of the x-term and squaring it. One value is added to form the perfect square trinomial, which is then rewritten as a squared binomial, while the other value is combined with the original constant term outside of the binomial.
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