Quadratic Functions

What does the graph of a quadratic function look like?

• A straight line

• A circle

• A parabola, which can open upwards or downwards

• An ellipse

Tags

CCSS.HSF-IF.C.7A

What is the significance of the y-intercept in a quadratic function?

• The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0) in the function.

• The y-intercept indicates the maximum value of the quadratic function.

• The y-intercept represents the slope of the function at its vertex.

• The y-intercept is the point where the graph crosses the x-axis.

Tags

CCSS.HSF-IF.C.7A

What does a zero discriminant indicate?

• A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

• A zero discriminant indicates that the quadratic equation has two distinct real roots.

• A zero discriminant indicates that the quadratic equation has no real roots.

• A zero discriminant indicates that the quadratic equation has complex roots.

Tags

CCSS.HSA-REI.B.4B

What is the standard form of a quadratic function?

• f(x) = ax² + bx + c

• f(x) = a(x - h)² + k

• f(x) = a(x + b)(x - c)

• f(x) = ax³ + bx² + c

What is the vertex form of a quadratic function?

• f(x) = a(x - h)² + k, where (h, k) is the vertex.

• f(x) = ax² + bx + c, where a, b, and c are constants.

• f(x) = a(x + h)² + k, where (h, k) is the vertex.

• f(x) = a(x - h)² - k, where (h, k) is the vertex.

What is the discriminant in a quadratic equation?

• The coefficient of the linear term in the equation.

• The part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

• The constant term in the equation.

• The sum of the roots of the equation.

Tags

CCSS.HSA-REI.B.4B

What is a quadratic function?

• A polynomial function of degree 1

• 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.

• A linear function represented by a straight line

• A function that has no real roots

How do you convert from standard form to vertex form?

• By using the quadratic formula.

• By completing the square.

• By factoring the equation.

• By graphing the function.

What is the maximum value of a quadratic function?

• The maximum value occurs at the vertex of the parabola when it opens downwards.

• The maximum value is always zero regardless of the parabola's orientation.

• The maximum value occurs at the x-intercepts of the parabola.

• The maximum value is found at the y-intercept of the parabola.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The highest or lowest point on the graph, depending on whether it opens upwards or downwards.

• The point where the parabola intersects the y-axis.

• The midpoint of the line segment connecting the focus and directrix.