Question

Sketch the graph of a quadratic function without using a graphic utility,identify the vertex,axis of symmetry and x intercept(s)-----g(x)=x^2-8

Answer 1

That's a parabola, as it can be written in the form \[y = ax^2+bx+c\]The x-coordinate of the vertex of a parabola in that form can be found by \[x = -\frac{b}{2a}\]

Answer 2

thanks mate

Answer 3

x-intercepts are the points where the curve crosses the x-axis, or y = 0.

Answer 4

but how to find the line of symmetry?

Answer 5

line of symmetry for a parabola is the perpendicular line going from vertex to directrix

Answer 6

\(\bf 4p(y-{\color{red}{ k}})=(x-{\color{red}{ h}})^2\qquad center=({\color{red}{ h,k}})
\\ \quad \\ \quad \\

g(x)=x^2-8\implies y=x^2-8\implies y+8=x^2
\\ \quad \\
\implies (y+8)=(x-0)^2\)