Answer :
Answer:
Refer the attached figure.
Step-by-step explanation:
Given : Quadratic function [tex]f(x)=2x^2+4x-16[/tex]
To find : The graph of the quadratic function using parabola tool?
Solution :
The given function [tex]f(x)=2x^2+4x-16[/tex]
First we find the vertex form of the equation
[tex]f(x)=2x^2+4x-16[/tex]
Where, a=2 ,b=4 , c=-16
Vertex is [tex]V=(\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
[tex]\frac{-b}{2a}=\frac{-4}{2(2)}=-1[/tex]
[tex]f(\frac{-b}{2a})=f(-1)=2(-1)^2+4(-1)-16=-18[/tex]
So, The vertex of the equation is (-1,-18)
Now, we find y- intercept by putting x=0 in the equation
[tex]y=2(0)^2+4(0)-16[/tex]
[tex]y=-16[/tex]
y- intercept (0,-16)
Now, we find x- intercept by putting y=0 in the equation
[tex]2x^2+4x-16=0[/tex]
[tex]x^2+2x-8=0[/tex]
[tex]x^2+4x-2x-8=0[/tex]
[tex]x(x+4)-2(x+4)=0[/tex]
[tex](x+4)(x-2)=0[/tex]
[tex]x=-4,2[/tex]
x- intercepts are (-4,0) and (2,0)
Placing all the points and plot a graph.
Refer the attached figure below.
