Question 1

How do I find the vertex of a parabola?

Accepted Answer

From y = ax² + bx + c, the x-coordinate of the vertex is h = -b / (2a). Plug h back into the equation to get the y-coordinate k. The vertex is (h, k).

Question 2

What is the axis of symmetry?

Accepted Answer

The vertical line through the vertex, x = -b / (2a). The parabola is a mirror image across it, so points equally far left and right of the axis have the same y-value.

Question 3

How do I know if the vertex is a maximum or minimum?

Accepted Answer

Look at the sign of a. If a is positive the parabola opens up and the vertex is the lowest point, a minimum. If a is negative it opens down and the vertex is the highest point, a maximum.

Question 4

How do I convert standard form to vertex form?

Accepted Answer

Find h and k as above, then write y = a(x - h)² + k. The calculator writes this out for you. Watch the sign: a vertex at x = 3 gives (x - 3)², and a vertex at x = -3 gives (x + 3)².

Question 5

Why are there no x-intercepts sometimes?

Accepted Answer

If the parabola opens up with its vertex above the x-axis, or opens down with its vertex below it, it never crosses. Algebraically, the discriminant b² - 4ac is negative.