Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

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

Front

What does the graph of a quadratic equation look like?

Back

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

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 whether it opens upwards or downwards.

Front

What is the Axis of Symmetry (AoS) in a quadratic graph?

Back

The Axis of Symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting y = 0 and solving the quadratic equation for x.

Front

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

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the roots, and then set each factor to zero.

Front

What is the area of a rectangle if the length is 8 units and the width is 3 units?

Back

The area is 8 * 3 = 24 square units.