Question 1

What is vertex form?

Accepted Answer

Vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a controls the width and direction. It makes it easy to identify the highest or lowest point of the parabola without any additional computation.

Question 2

How do I convert standard form to vertex form?

Accepted Answer

Calculate h = -b/(2a) and k = c - b²/(4a). For y = x² + 8x + 12: h = -8/2 = -4, k = 12 - 64/4 = 12 - 16 = -4. So vertex form is y = (x + 4)² - 4. You can also complete the square to arrive at the same result.

Question 3

What is the axis of symmetry?

Accepted Answer

The axis of symmetry is the vertical line x = h that passes through the vertex. Every parabola is symmetric about this line, meaning for any point on one side, there is a mirror-image point on the other. For y = 3(x - 5)² + 2, the axis of symmetry is x = 5.

Question 4

How do I tell if a parabola opens up or down?

Accepted Answer

Look at the coefficient a. If a > 0, the parabola opens upward and the vertex is the minimum point. If a < 0, it opens downward and the vertex is the maximum. The larger the absolute value of a, the narrower the parabola.

Question 5

Is vertex form the same as completing the square?

Accepted Answer

Completing the square is the algebraic process used to derive vertex form. The end result is the same equation y = a(x - h)² + k. This calculator uses the direct formulas h = -b/(2a) and k = c - b²/(4a), which are equivalent to completing the square but faster to compute.

Vertex Form Calculator

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