Standard to Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a parabola given in standard form?

Back

To find the vertex of a parabola in standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

Convert the standard form equation y = 2x² + 8x + 6 to vertex form.

Back

y = 2(x + 2)² - 2.

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

How do you convert from vertex form to standard form?

Back

Expand the vertex form f(x) = a(x - h)² + k to get the standard form f(x) = ax² + bx + c.

Front

What is the significance of the vertex in a parabola?

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upward or downward.

Front

Convert the equation y = (x - 3)² + 5 into standard form.

Back

y = x² - 6x + 14.

Front

What is the formula to convert from standard form to vertex form?

Back

Use the method of completing the square to rewrite the standard form equation into vertex form.

Front

If a parabola opens downward, what can you say about the 'a' value?

Back

If a parabola opens downward, the 'a' value in the vertex form is negative (a < 0).