5.21 - Vertex Form of Quadratics

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 variable 'a' represent in the vertex form of a quadratic?

Back

The variable 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

How do you find the axis of symmetry from the vertex form?

Back

The axis of symmetry can be found using the formula x = h, where h is the x-coordinate of the vertex.

Front

What is the significance of the vertex in a quadratic function?

Back

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

Front

If a = 2 in the vertex form y = 2(x - 3)² + 1, what is the direction of the parabola?

Back

The parabola opens upwards because a is positive.

Front

What does the value of 'h' indicate in the vertex form?

Back

The value of 'h' indicates the x-coordinate of the vertex and the axis of symmetry.

Front

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

Back

You can convert by completing the square.

Front

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

Back

Changing 'k' shifts the parabola vertically; increasing 'k' moves it up, while decreasing 'k' moves it down.

Front

What is the axis of symmetry for the quadratic equation y = 3(x - 4)² + 2?

Back

The axis of symmetry is x = 4.

Front

If the vertex of a parabola is at (2, -3), what is the vertex form of the equation if a = 1?

Back

The vertex form is y = (x - 2)² - 3.