Question

How do you find the vertex and axis of symmetry, and then graph the parabola given by: `f(x)= -4(x - 8)^2 + 3`?

Answer 1

You have the right form (vertex form). All that you have left to do is learn what parts of the equation signify what.

Explanation:

In a quadratic function of form y = a`(x - p)^2` + q, the axis of symmetry is found at x = p. As a result, in y = -4`(x - 8)^2` + 3, the axis of symmetry is at x = 8, since the formula is x - p = x - (+8).

The vertex of a parabola is at (p, q). As for the axis of symmetry, the p value is 8, and in this function the q value is 3. So the vertex is at (8,3).

With this information, the x and y intercepts, and a few other points found by plugging in x values and solving for y, you will be able to graph this parabola. Your graph, if done properly, will look like the following:

graph{y = -4(x - 8)^2 + 3 [-20, 20, -10, 10]}