1. y-intercept
[tex]\boxed{(0,-10)}[/tex]
The quadratic function [tex]f(x)=2x^22-8x-10[/tex] represents a parabola. In fact, the graph of a quadratic function is a special type of U-shaped curve called a parabola. To find the y intercept, we set [tex]x=0[/tex] as follows:
[tex]f(x)=2x^2-8x-10 \\ \\ If \ x=0 \rightarrow f(0)=-10 \\ \\ Then \ y-intercept: \\ \\ (0,-10)[/tex]
2. x-intercepts
[tex]\boxed{(-1,0) \ and \ (5,0)}[/tex]
To find the other x-intercept, we must set [tex]y=0[/tex] as follows:
[tex]f(x)=2x^2-8x-10 \\ \\ If \ y=0 \rightarrow 2x^2-8x-10=0 \\ \\ Using \ the \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \therefore x=\frac{-(-8) \pm \sqrt{(-b)^2-4(2)(-10)}}{2(2)} \\ \\ \therefore x_{1}=-1 \ and \ x_{2}=5[/tex]
Therefore, the other x-intercept is [tex](5,0)[/tex]. You can see both the y-intercept and the x-intercepts in the figure below.
