Step 1
Given;
[tex]f(x)=x^2+2x-8[/tex]
Required; To find the vertex and axes intercepts. write it in standard form and graph it.
Step 2
Find the vertex
[tex]\begin{gathered} (h,k)=(\frac{-b}{2a},f(h)) \\ a=1,b=2,c=-8 \end{gathered}[/tex][tex]\begin{gathered} h=-\frac{2}{2(1)}=-1 \\ f(h)=(-1)^2+2(-1)-8=1-2-8=-9 \\ Vertex(h,k)=(-1,-9) \end{gathered}[/tex]
Step 3
Find the axes intercepts
[tex]\begin{gathered} x^2+2x-8=0 \\ factors\text{ are 4x and -2x} \\ x^2+4x-2x-8=0 \\ x(x+4)-2(x+4)=0 \\ (x-2)(x+4)=0 \\ x=2\text{ or -4} \\ x-intercepts=(-4,0),(2,0) \end{gathered}[/tex][tex]\begin{gathered} To\text{ find the y-intercept set x=0} \\ f(x)=0^2+2(0)-8 \\ f(x)=-8 \\ y-intercept=(0,-8) \end{gathered}[/tex]
Step 4
Graph the function.
Step 5
The standard form will be;
[tex]\begin{gathered} f(x)=ax^2+bx+c-\text{ Standard form of any quadratic eqaution} \\ Thus\text{ the required standard form will be;} \\ f(x)=x^2+2x-8 \end{gathered}[/tex]
