Transformations of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What does it mean for a quadratic function to be 'reflected over the x-axis'?

Back

A quadratic function is reflected over the x-axis when the coefficient 'a' is negative, causing the parabola to open downwards.

Front

How does changing the value of 'a' affect the graph of a quadratic function?

Back

Changing the value of 'a' affects the width and direction of the parabola. A larger |a| makes the parabola narrower, while a smaller |a| makes it wider.

Front

What is the effect of adding a constant 'k' to a quadratic function?

Back

Adding a constant 'k' to a quadratic function shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

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 equation x = -b/2a.

Front

What does it mean for a quadratic function to be 'stretched' or 'compressed'?

Back

A quadratic function is 'stretched' when |a| > 1, making it narrower, and 'compressed' when 0 < |a| < 1, making it wider.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating f(0), which gives the point where the graph intersects the y-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B