BenoguigoliB

2021-01-30

Use the following quadratic function to answer the question below: $y={x}^{2}-14x+5$

a. Showing all work, find the vertwx of the quadratic.

b. Write the quadratic in the vertex form

a. Showing all work, find the vertwx of the quadratic.

b. Write the quadratic in the vertex form

Alix Ortiz

Skilled2021-01-31Added 109 answers

(a) find the vertex of the quadratic.

the quadratic function can be written as:

$y={x}^{2}-14x+5$

$y={x}^{2}-14x+{7}^{2}-{7}^{2}+5$

$y={x}^{2}-2\left(x\right)\left(7\right)+{7}^{2}-49+5$

$y={(x-7)}^{2}-44$ (1)

as we know that the quadratic function$y=a{x}^{2}+bx+c$ in standard form can be written in vertex form having vertex at (h,k) as:

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

therefore by comparing (1) with the equation$y=a{(x-h)}^{2}+k$ , we get

a=1, h=7 and k=−44

therefore the vertex of the quadratic is (h,k)=(7,−44)

(b) write the quadratic in vertex form.

the equation (1) is the equation of the quadratic in vertex form.

therefore the equation of the given quadratic in vertex form is:

$y={(x-7)}^{2}-44$

the quadratic function can be written as:

as we know that the quadratic function

therefore by comparing (1) with the equation

a=1, h=7 and k=−44

therefore the vertex of the quadratic is (h,k)=(7,−44)

(b) write the quadratic in vertex form.

the equation (1) is the equation of the quadratic in vertex form.

therefore the equation of the given quadratic in vertex form is:

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