Vertex-Form

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the vertex from the vertex form equation y = a(x - h)² + k?

Back

The vertex of the parabola is the point (h, k).

Front

What does the 'a' in the vertex form equation y = a(x - h)² + k represent?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the effect of changing the value of 'a' in the vertex form equation?

Back

Changing 'a' affects the width of the parabola. Larger absolute values of 'a' make the parabola narrower, while smaller absolute values make it wider.

Front

How do you convert the standard form of a quadratic equation to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

Front

What is the vertex of the parabola given by the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).

Front

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

Back

The graph opens downward when the coefficient of x² is negative.

Front

Convert the equation y = x² + 4x + 11 into vertex form.

Back

The vertex form is y = (x + 2)² + 7.

Front

What is the vertex of the parabola represented by the equation y = -(x - 1)² + 4?

Back

The vertex is (1, 4).

Front

Which equation represents the vertex form of a quadratic?

Back

The vertex form is y = a(x - h)² + k.