Flashcard 5.1-5.2. Solve Quadratic Functions

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 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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

A quadratic function has real roots if the discriminant (b² - 4ac) is greater than or equal to zero.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The x-intercepts of a quadratic function can be found by setting the function equal to zero and solving for x.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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, located at the point (h, k) where h = -b/(2a) and k = f(h).

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, given by the equation x = -b/(2a).

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 distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the roots x = p and x = q.

Tags

CCSS.HSA-REI.B.4B

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.