Question

Nick wrote the function p(x) = 17 42x – 7x2 in vertex form. His work is below. P(x) = –7x2 42x 17 p(x) = –7(x2 – 6x) 17 (StartFraction negative 6 Over 2 EndFraction) squared = 9; p(x) = –7(x2 – 6x 9) 17 p(x) = –7(x – 3)2 17 When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake? In step 1, he did not put the function in standard form correctly. In step 2, he should have also factored –7 from the constant term, 17. In step 3, he did not subtract –7(9) to keep the function equivalent. In step 4, he did not write the perfect square trinomial correctly as a binomial squared.

Answer 1

Quadratic equations are second-order equations.  Nick made In step 3 when he did not subtract –7(9) to keep the function equivalent.

What is a Quadratic Equation?

A quadratic equation is an equation that can be written in the form of

ax²+bx+c.

Where a is the leading coefficient, and

c is the constant.

In order to find the mistake that Nick made, we will first find the factors ourselves, therefore, we will factorize the trinomial,

$17+42x-7x^2 = 9\\\\17+42x-7x^2 - 9 =0\\\\-7x^2 +42x +11 = 0\\\\-7x(x +6) +11 = 0$

If we compare our process with Nick's process, we observe In step 3, he did not subtract –7(9) to keep the function equivalent

Hence, Nick made In step 3, when he did not subtract –7(9) to keep the function equivalent.

Learn more about Quadratic Equation:

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