Vertex Form Flashcard

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 axis of symmetry in vertex form?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex in the vertex form y = a(x - h)² + k.

Front

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

Back

The 'a' value indicates 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 vertex of the function y = 2(x - 5)² + 6?

Back

The vertex is (5, 6).

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value at the vertex. If 'a' is negative, the function has a maximum value at the vertex.

Front

What is the axis of symmetry for the function y = 1/2(x + 4)² - 5?

Back

The axis of symmetry is x = -4.

Front

Sketch the graph of y = -2(x + 5)² + 2. What type of vertex does it have?

Back

The graph opens downwards, and the vertex is a maximum point.

Front

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

Back

Changing the 'h' value shifts the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Front

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

Back

Changing the 'k' value shifts the graph vertically. If 'k' increases, the graph shifts up; if 'k' decreases, it shifts down.

Front

Given the function y = 2(x + 4)² - 4, what is the vertex?

Back

The vertex is (-4, -4).