Graphing Quadratics

Front

What is a quadratic function?

Back

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

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which f(x) = 0. They can be found by factoring, using the quadratic formula, or completing the square.

Front

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

Back

The y-intercept of a quadratic function f(x) = ax^2 + bx + c is found by evaluating f(0), which gives the point (0, c) on the graph.

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. It can be found using the formula x = -b/(2a) for the x-coordinate.

Front

What does it mean for a quadratic to be in standard form?

Back

A quadratic is in standard form when it is expressed as f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the axis of symmetry 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 using the formula x = -b/(2a).

Front

What is the difference between maximum and minimum values in quadratics?

Back

A maximum value occurs at the vertex of a downward-opening parabola, while a minimum value occurs at the vertex of an upward-opening parabola.

Front

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

Back

The x-intercepts can be found by setting f(x) = 0 and solving for x, often using factoring, the quadratic formula, or completing the square.

Front

What is the quadratic formula?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, and it determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.