what is the axis of symmetry for the function (x)=5x^2+8?

Question

x=_________

alegebra 1

Answer 1

Hey there,

The axis of symmetry in this case will be the y-axis. To illustrate, recall the general form of a quadratic function:

f(x) = a(x - h)^2 + k

where the vertex is located at (h,k), or the point (0,8) (h = 0 and k = 8). Because the vertex lies on the y-axis, and opens upward, the y-axis must be its line of symmetry.

Try graphing it on Desmos or some other graphing software if you are having any trouble visualizing it.

Hope that helps!

Answer 2

If f(x) = 5x² + 8 then to find the line of symmetry, we could find the vertex and the line of symmetry would then be x = (whatever the x coordinate of the vertex is).

The vertex of a quadratic equation can be found from x = -b/(2a) but in this case, since there is no "x" value, the b = 0. So x = 0/(whatever) = 0 meaning the line of symmetry is x = 0

Answer 3

For a quadratic function in the form of y= ax² + bx + c, the axis of symmetry is a vertical line with the equation x= -b/2a

In the standard quadratic formula form, the equation in this problem is 5x² -x + 8

The axis of symmetry is:

x = -b/2a

x = 1/2(5)

x = 1/10