Quadratics Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

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

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. It can be found using the formula x = -b/2a.

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

The 'a' value determines the direction and width of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards. A larger |a| value makes the parabola narrower.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

You can determine the direction by looking at the 'a' value in the quadratic function: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.