Mastering Polynomials

(x + 2)(x + 3)

(x - 1)(x - 6)

(x - 2)(x - 3)

(x - 4)(x - 2)

11

5

9

15

The vertex of the graph is at (2, 0) and opens downwards.

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 x-intercepts are at (-1, 0) and (1, 0).

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

3(x + 2)^2

3(x + 4)(x + 1)

(3x + 6)(x + 2)

(x + 3)(3x + 4)

1

2

0

-1

The graph of g(x) = -x^3 + 3x has a local minimum at (0, 0) and is symmetric about the x-axis.

The graph of g(x) = -x^3 + 3x is a cubic curve with a local maximum at (0, 0) and symmetric behavior about the y-axis.

The graph of g(x) = -x^3 + 3x is a quadratic curve with a minimum at (0, 0).

The graph of g(x) = -x^3 + 3x is a linear function with no maximum points.

(x + 1)(x + 10)

(x + 3)(x + 4)

(x + 2)(x + 5)

(x - 2)(x - 5)

0

5

3

-4

The graph of h(x) = 2x^4 - x^2 + 1 is a quartic polynomial that opens upwards with a minimum point and no x-intercepts.

The graph of h(x) = 2x^4 - x^2 + 1 is a linear function with one x-intercept.

The graph of h(x) = 2x^4 - x^2 + 1 has two x-intercepts and no minimum point.

The graph of h(x) = 2x^4 - x^2 + 1 is a cubic polynomial that opens downwards.

4(x - 2)(x + 2)

4(x - 4)(x + 4)

2(x - 2)(x + 2)

(x - 2)(x - 2)