Mastering Quadratic Equations

Solve for x: x^2 - 5x + 6 = 0.

• x = 2, x = 3

• x = 5

• x = 4

• x = 1

Graph the function: f(x) = x^2 - 4.

• The vertex of the graph is at (0, 0) with no x-intercepts.

• The graph of f(x) = x^2 - 4 is a parabola opening upwards with vertex at (0, -4) and x-intercepts at (-2, 0) and (2, 0).

• The graph of f(x) = x^2 - 4 is a straight line with a slope of 2.

• The graph opens downwards and has a vertex at (0, 4).

Identify the vertex of the quadratic: y = 2x^2 + 8x + 3.

• (-1, 2)

• (0, 3)

• (-3, -4)

• (-2, -5)

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

• (x + 2)(x + 5)

• (x + 1)(x + 10)

• (x + 3)(x + 4)

• (x - 2)(x - 5)

Use the quadratic formula to solve: 3x^2 - 12x + 9 = 0.

• x = -1, 5

• x = 1, 3

• x = 0, 4

• x = 2, 2

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

• x = 4

• x = 0

• x = 3

• x = 2

Graph the function: f(x) = -2x^2 + 4x + 1.

• The vertex of the parabola is at (0, 1) with no x-intercepts.

• The graph is an upward-opening parabola with vertex at (1, 1).

• The graph of the function is a downward-opening parabola with vertex at (1, 3), y-intercept at (0, 1), and x-intercepts at (2, 0) and (-0.5, 0).

• The y-intercept is at (0, 4) and x-intercepts at (1, 0) and (3, 0).

Factor the quadratic: x^2 - 9.

• (x - 9)(x + 1)

• (x + 3)(x + 3)

• (x - 6)(x + 6)

• (x - 3)(x + 3)

Find the roots of the equation: 4x^2 + 4x + 1 = 0 using the quadratic formula.

• -1

• 0

• 1/2

• -1/2

• -3/2

Identify the vertex of the function: y = x^2 - 2x + 1.

• (1, 0)

• (1, 1)

• (2, 1)

• (0, 1)