Quadratics - Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

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

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 find the vertex from the vertex form?

Back

The vertex can be found directly from the vertex form y = a(x-h)² + k as (h, k).

Front

What is the effect of changing 'h' in the vertex form?

Back

Changing 'h' translates the parabola horizontally. If h is increased, the parabola moves to the right; if h is decreased, it moves to the left.

Front

What is the effect of changing 'k' in the vertex form?

Back

Changing 'k' translates the parabola vertically. If k is increased, the parabola moves up; if k is decreased, it moves down.

Front

What is the vertex of the parabola: y=2(x-3)²+4?

Back

The vertex is (3, 4).

Front

Explain the translation of the parabola: y = (x - 5)² - 1.

Back

The parabola is translated right 5 units and down 1 unit.

Front

Explain the translation of the parabola: y = (x + 14)².

Back

The parabola is translated left 14 units.

Front

What causes the graph of y = x² to open downward?

Back

The graph opens downward if the x² term is multiplied by a negative number.

Front

What is the axis of symmetry for the parabola in vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.