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.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B