Vertex form quadratics

Front

What does the h term tell you in vertex form quadratics?

Back

The h term indicates the horizontal shift of the parabola. It tells you the direction (left or right) and is the opposite sign of the value. It also represents the x-value of the vertex and the axis of symmetry.

Front

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

Back

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

Front

What is the quadratic parent function of y = x² shifted right 7 units?

Back

The function is y = (x - 7)².

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

How do we transform from the parent function y = x² to y = -1/5(x - 1)² + 7?

Back

The transformation involves a reflection across the x-axis, vertical compression, a horizontal shift to the right by 1 unit, and a vertical shift up by 7 units.

Front

What does the a term represent in vertex form quadratics?

Back

The a term represents the vertical stretch or compression and the direction of the parabola (upward if a > 0, downward if a < 0).

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 is the x-coordinate of the vertex.

Front

What is the effect of changing the value of h in the vertex form y = a(x - h)² + k?

Back

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

Front

What does the k term indicate in vertex form quadratics?

Back

The k term indicates the vertical shift of the parabola. It represents the y-coordinate of the vertex.

Front

How do you determine if a parabola opens upward or downward?

Back

A parabola opens upward if the a value in the vertex form y = a(x - h)² + k is positive, and it opens downward if a is negative.