2024 Unit 3 Quadratic Functions Review Test

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7A

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 are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the values of x for which f(x) = 0, found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic function tell us?

Back

The discriminant, given by b² - 4ac, indicates 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

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

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

Back

A quadratic function opens upwards if a > 0 and downwards if a < 0 in the standard form f(x) = ax^2 + bx + c.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola: larger |a| values make it narrower, while smaller |a| values make it wider.

Tags

CCSS.HSF-IF.C.7A