Mastering Quadratic Functions

What is the standard form of a quadratic function?

• f(x) = a^2 + bx + c

• f(x) = ax^2 + bx + c

• f(x) = ax^2 + b + c

• f(x) = ax + bx^2 + c

Identify whether the function f(x) = 2x^2 - 3x + 1 is a quadratic function.

• No, f(x) is a linear function.

• Yes, f(x) is a cubic function.

• Yes, f(x) is a quadratic function.

• No, f(x) is a constant function.

Graph the quadratic function y = x^2 - 4. What is the shape of the graph?

• The shape of the graph is a straight line.

• The shape of the graph is a parabola that opens downwards.

• The shape of the graph is a circle.

• The shape of the graph is a parabola that opens upwards.

Solve the quadratic equation x^2 - 5x + 6 = 0.

• x = -2, x = -3

• x = 0, x = 5

• x = 2, x = 3

• x = 1, x = 6

Factor the quadratic expression x^2 + 7x + 10.

• (x + 2)(x + 5)

• (x - 2)(x - 5)

• (x + 1)(x + 10)

• (x + 3)(x + 4)

Determine the vertex of the quadratic function f(x) = -2x^2 + 4x - 1.

• (1, 1)

• (2, 3)

• (0, -1)

• (-1, 0)

What is the axis of symmetry for the function f(x) = 3x^2 + 6x + 2?

• 1

• -1

• -2

• 0

Identify the roots of the quadratic equation 2x^2 + 8x + 6 = 0 using the quadratic formula.

• x = -2 and x = -4

• x = 0 and x = -6

• x = 1 and x = 3

• The roots are x = -1 and x = -3.

Graph the function y = -x^2 + 2x + 3. What are the coordinates of the vertex?

• (1, 4)

• (1, 2)

• (0, 3)

• (2, 5)

Factor the expression 4x^2 - 12x + 9.

• (2x + 3)(2x - 3)

• (4x - 9)(x + 1)

• (2x - 3)^2

• (4x^2 - 6x + 3)(x - 1)