Quadratic Transformations 3

Front

What is the x-intercept of a graph?

Back

The x-intercept is the point where a graph touches or crosses the x-axis.

Front

What happens to the graph of f(x) = x² when it is replaced with f(x) + 2?

Back

The graph undergoes a vertical translation up by 2 units.

Front

True or False: The x-intercepts, zeros, and roots/solutions of a quadratic function are all equal.

Back

True.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a function to have a zero?

Back

A zero is an x-value that makes the function equal 0 when plugged in.

Tags

CCSS.HSF-IF.C.7C

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function.

Front

If f(x) = x² and we replace it with f(x) - 3, what transformation occurs?

Back

The graph moves down 3 units.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in the quadratic function affect?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B