Vertex form quadratics

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 identify 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

In the equation y = 3(x + 5)² - 4, what is the vertex?

Back

The vertex is (-5, -4).

Front

What do the parameters a, h, and k represent in the vertex form of a quadratic?

Back

In the vertex form y = a(x - h)² + k: a affects the width and direction of the parabola, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

Front

What transformation occurs when the value of a is greater than 1 in the vertex form?

Back

The parabola becomes narrower compared to the parent function y = x².

Front

What transformation occurs when the value of a is between 0 and 1 in the vertex form?

Back

The parabola becomes wider compared to the parent function y = x².

Front

What does a negative value of a indicate in the vertex form?

Back

A negative value of a indicates that the parabola opens downwards.

Front

How do you transform the parent function y = x² to y = 2x² + 4?

Back

The transformation involves a vertical stretch by a factor of 2 and a vertical translation up by 4.

Front

What is the effect of the transformation from y = x² to y = -1/5(x - 1)² + 7?

Back

This transformation includes a reflection over the x-axis, a vertical compression by a factor of 5, a horizontal shift right by 1, and a vertical shift up by 7.

Front

How do you find the value of k in the vertex form equation?

Back

The value of k is the y-coordinate of the vertex in the vertex form equation y = a(x - h)² + k.