Question

Function: y = x² + 5x - 7Vertex:Solutions:) and

Answer 1

For a quadratic function of the form:

`\begin{gathered} y=ax^2+bx+c \\ the_{\text{ }}vertex: \\ V=(h,k) \\ can_{\text{ }}be_{\text{ }}found_{\text{ }}as_{\text{ }}follows: \\ h=-(b)/(2a) \\ k=y(h) \end{gathered}`

So, for:

`\begin{gathered} y=x^2+5x-7 \\ a=1 \\ b=5 \\ c=-7 \end{gathered}`
`\begin{gathered} h=-(5)/(2(1))=-(5)/(2)=-2.5 \\ k=y(2.5)=(-2.5^2)+5(-2.5)-7=-13.25 \end{gathered}`

Therefore, the vertex is:

V = (-2.5,-13.25)

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The solutions can be found using the quadratic formula:

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ \\ x=(-5\pm√(5^2-4(1)(-7)))/(2(1)) \\ \\ x=(-5\pm√(53))/(2) \end{gathered}`

Therefore, the solutions are:

`\begin{gathered} x=(-5+√(53))/(2)\approx1.14 \\ and \\ x=(-5-√(53))/(2)\approx-6.14 \end{gathered}`