Given the function
[tex]f(x)=2x^2+2x-24[/tex]To find the x and y intersects of the parabola you have to do as follows:
y-intercept
This is the value of f(x) when x=0, to find it replace the value in the formula:
[tex]\begin{gathered} f(0)=2(0)^2+2\cdot0-24 \\ f(0)=-24 \end{gathered}[/tex]The y-intercept of the parabola is (0,-24)
Vertex
Calculate the x coordinate using the following formula:
For
[tex]y=ax^2+bx+c[/tex][tex]x_v=-\frac{b}{2a}[/tex]For this function:
[tex]x_v=-\frac{2}{2\cdot2}=-\frac{2}{4}=-\frac{1}{2}[/tex]Using this value of x imput it in the formula to reach the value of the y-coordinate of the vertex:
[tex]\begin{gathered} f(x_v=-\frac{1}{2})=2(-\frac{1}{2})^2+2(-\frac{1}{2})-24 \\ f(x_v)=-\frac{49}{2} \end{gathered}[/tex]The vertex is (-1/2,-49/2)
Using these two points you can draw the function:
Using the graph you can determine the x-intercepts of the function, these are (-4,0) and (3,0)
