Understanding Quadratic Functions

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = ax^3 + bx + c

• f(x) = ax^2 + b

• f(x) = a + b + c

Identify the vertex of the quadratic function y = x^2 - 4x + 3.

• (3, 0)

• (1, 2)

• (0, 3)

• (2, -1)

What is the axis of symmetry for the function y = 2x^2 + 8x + 6?

• x = 0

• x = -2

• x = 2

• x = -4

How do you determine the direction of the parabola in a quadratic function?

• The direction is based on the vertex's position in the coordinate plane.

• The direction of the parabola is determined by the sign of the coefficient 'a' in the quadratic function.

• The parabola opens to the right if 'c' is positive.

• The direction is determined by the value of 'b' in the quadratic function.

What is the quadratic formula used for?

• To determine the slope of a line.

• To solve linear equations.

• To find the roots of a quadratic equation.

• To calculate the area of a triangle.

Calculate the roots of the equation x^2 - 5x + 6 = 0.

• x = 1, x = 6

• x = -2, x = -3

• x = 2, x = 3

• x = 0, x = 5

What does the discriminant tell you about the roots of a quadratic equation?

• The discriminant shows the vertex of the parabola.

• The discriminant determines the slope of the quadratic function.

• The discriminant tells you the nature of the roots: two distinct real roots, one real root, or two complex roots.

• The discriminant indicates the sum of the roots.

Explain how to complete the square for the function y = x^2 + 6x + 5.

• y = (x + 3)^2 - 4

• y = (x + 2)^2 + 1

• y = (x + 4)^2 - 3

• y = (x - 3)^2 + 5

What is the maximum or minimum value of the function y = -3x^2 + 12x - 5?

• 5

• 10

• 7

• -3

How can you graph a quadratic function using its intercepts?

• Graph the quadratic function by plotting its x-intercepts and y-intercept, then sketch the parabola.

• Use only the y-intercept to sketch the graph.

• Draw a straight line through the intercepts.

• Graph the function by only plotting the vertex.