Quadratic Transformations

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 and a ≠ 0.

Front

What is the vertex of a parabola?

Back

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

Front

What does the term 'axis of symmetry' refer to in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found at x = -b/2a.

Front

How does the graph of y = x² change when we add a constant to it?

Back

Adding a constant 'k' to the function y = x² results in a vertical shift of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What effect does a negative coefficient in front of x² have on the parabola?

Back

A negative coefficient in front of x² causes the parabola to open downwards, creating a maximum point at the vertex.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

How do you find the zeros of a quadratic function?

Back

The zeros of a quadratic function can be found by factoring, using the quadratic formula, or by completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.

Front

What does it mean for a quadratic function to have two real roots?

Back

A quadratic function has two real roots if the discriminant (b² - 4ac) is greater than zero, indicating two distinct x-intercepts.