Question

Write h(x) = 7 10x x2 in vertex form. Write h in standard form. H(x) = x2 10x 7 Form a perfect square trinomial by adding and subtracting StartFraction b Over 2 EndFraction squared. H(x) = (x2 10x 25) 7 – 25 Write the trinomial as a binomial squared. Write the function in vertex form, if needed. What is h(x) = 7 10x x2 written in vertex form? h(x) = (x – 25)2 – 18 h(x) = (x – 5)2 32 h(x) = (x 5)2 – 18 h(x) = (x 25)2 32.

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

You can use the definition for the vertex form of a quadratic equation and then can can do conversion of that quadratic equation in that form.

The correct vertex form of the given equation is given by

Option C: $h(x) = (x-5)^2 - 18$

What is vertex form of  a quadratic equation?

If a quadratic equation is written in the form

$y = a(x-h)^2 + k$

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point is called the vertex of the parabola that quadratic equation represents.

How to convert the given equation to vertex form?

We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

The given equation is $h(x) = 7 + 10x + x^2$

Converting it in vertex form, we get:

$h(x) = 7 + 10x + x^2\\\\\\h(x) = x^2 + 10x + 7\\h(x) = x^2 + 10x + 25 -25 + 7\\h(x) = (x+5)^2 - 18 \text{\: (Note how the form} \: a^2 + b^2 + 2ab = (a+b)^2 \:\rm got\: made)$

Thus, we have h = -5 and k = -18

The plot of the given equation is attached below.

Thus,

The correct vertex form of the given equation is given by

Option C: $h(x) = (x-5)^2 - 18$

Learn more about vertex form of quadratic equations here:
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