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

Question
Use the following quadratic function to answer the question below: \(\displaystyle{y}={x}^{{2}}-{14}{x}+{5}\)
a. Showing all work, find the vertwx of the quadratic.
b. Write the quadratic in the vertex form

Answers (1)

2021-01-31
(a) find the vertex of the quadratic.
the quadratic function can be written as:
\(\displaystyle{y}={x}^{{2}}−{14}{x}+{5}\)
\(\displaystyle{y}={x}^{{2}}−{14}{x}+{7}^{{2}}−{7}^{{2}}+{5}\)
\(\displaystyle{y}={x}^{{2}}−{2}{\left({x}\right)}{\left({7}\right)}+{7}^{{2}}−{49}+{5}\)
\(\displaystyle{y}={\left({x}−{7}\right)}^{{2}}−{44}\) (1)
as we know that the quadratic function \(\displaystyle{y}={a}{x}^{{2}}+{b}{x}+{c}\) in standard form can be written in vertex form having vertex at (h,k) as:
\(\displaystyle{y}={a}{\left({x}−{h}\right)}^{{2}}+{k}\)
therefore by comparing (1) with the equation \(\displaystyle{y}={a}{\left({x}−{h}\right)}^{{2}}+{k}\), 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:
\(\displaystyle{y}={\left({x}−{7}\right)}^{{2}}−{44}\)
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