# 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

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
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Alix Ortiz
(a) find the vertex of the quadratic.
the quadratic function can be written as:
$y={x}^{2}-14x+5$
$y={x}^{2}-14x+{7}^{2}-{7}^{2}+5$
$y={x}^{2}-2\left(x\right)\left(7\right)+{7}^{2}-49+5$
$y={\left(x-7\right)}^{2}-44$ (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:
$y=a{\left(x-h\right)}^{2}+k$
therefore by comparing (1) with the equation $y=a{\left(x-h\right)}^{2}+k$, 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:
$y={\left(x-7\right)}^{2}-44$