Solving Quadratic Equations: Completing the Square (Continued) Answers
What are the values of the coefficients and constant term of 0 = 4 – 7x2 + x in standard form? a = b = c =
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Which equations have a leading coefficient of 3 and a constant term of –2? Check all that apply. 0 = 3x2 + 2x – 20 = –2 – 3x2 + 30 = –3x + 3x2 – 2 0 = 3x2 + x + 20 = –1x – 2 + 3x2
Which operation is performed in the derivation of the quadratic formula moving from Step 6 to Step 7?
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Consider the function f(x) = 3x2 + 7x + 2. What is the value of the discriminant? How many x-intercepts does this function have? What are the number of zeros for this function?
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Which values of c will cause the quadratic equation –x2 + 3x + c = 0 to have no real number solutions? Check all that apply. –51
Describe how to derive the quadratic formula from a quadratic equation in standard form.
To derive the quadratic formula, start with the standard form of a quadratic equation, ax^2 + bx + c = 0. Divide the entire equation by a, then move the constant term c to the other side. Complete the square by adding (b/2a)^2 to both sides of the equation. This allows you to factor the left side as a perfect square trinomial. Finally, take the square root of both sides and isolate x to arrive at the quadratic formula.
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What did you include in your response? Check all that apply.
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