Polynomial Functions Graphing

Graph the polynomial function f(x) = x^2 - 4x + 4

• The vertex of the graph is at (0, 2).

• The graph is a straight line with a positive slope.

• The graph is a parabola opening upwards with the vertex at (2, 0).

• The graph is a parabola opening downwards.

Identify the x-intercepts of the polynomial function g(x) = (x-3)(x+2)

• x = 1, x = -5

• x = 4, x = -3

• x = 3, x = -2

• x = 0, x = -1

Sketch the graph of the polynomial h(x) = -2x^3 + 3x^2 - 6x

• The graph will be a straight line.

• The graph will start in the third quadrant, pass through the origin, and end in the first quadrant.

• The graph will start in the first quadrant and end in the fourth quadrant.

• The graph will have no x-intercepts.

Determine the end behavior of the polynomial function k(x) = 4x^4 - 2x^3 + 5x - 1

• As x approaches negative infinity, k(x) approaches positive infinity. As x approaches positive infinity, k(x) also approaches positive infinity.

• As x approaches negative infinity, k(x) approaches zero. As x approaches positive infinity, k(x) also approaches zero.

• As x approaches negative infinity, k(x) approaches negative infinity. As x approaches positive infinity, k(x) also approaches negative infinity.

• As x approaches negative infinity, k(x) approaches positive infinity. As x approaches positive infinity, k(x) approaches negative infinity.

Find the y-intercept of the polynomial function p(x) = 2x^2 + 8x - 6

• 4

• -8

• 10

• -6

Plot the graph of the polynomial function q(x) = x^3 - 2x^2 - 8x + 16

• The x-intercepts are x = 0, x = 4, and the vertex is at (2, 10). The graph is a quartic function that intersects the x-axis at x = 0, x = 4, and has a maximum point at (2, 10).

• The x-intercepts are x = -2, x = 2, and the vertex is at (1, 7). The graph is a cubic function that intersects the x-axis at x = -2, x = 2, and has a minimum point at (1, 7).

• The x-intercepts are x = -1, x = 1, and the vertex is at (-2, 5). The graph is a quadratic function that intersects the x-axis at x = -1, x = 1, and has a maximum point at (-2, 5).

• The x-intercepts are x = -3, x = 3, and the vertex is at (0, 8). The graph is a cubic function that intersects the x-axis at x = -3, x = 3, and has a minimum point at (0, 8).

Calculate the turning points of the polynomial function r(x) = x^4 - 4x^3 + 4x^2

• (3, 0)

• (0, 1)

• (2, 2)

• (0, 0), (2, 0), (1, 1)

Graph the polynomial function s(x) = -x^3 + 2x^2 - 3x + 1

• Graph the quadratic function s(x) = x^2 - 3x + 1

• Graph the linear function s(x) = -x + 1

• Graph the exponential function s(x) = 2^x

• Graph the polynomial function s(x) = -x^3 + 2x^2 - 3x + 1 on a coordinate plane.

Identify the degree and leading coefficient of the polynomial function t(x) = 5x^5 - x^3 + 2x

• {'degree': 5, 'leading_coefficient': 5}

• {'degree': 4, 'leading_coefficient': 2}

• {'degree': 3, 'leading_coefficient': 5}

• {'degree': 5, 'leading_coefficient': 3}

Sketch the graph of the polynomial u(x) = 3x^2 - 6x + 9

• The graph of the polynomial u(x) = 3x^2 - 6x + 9 is a circle centered at (0, 0).

• The graph of the polynomial u(x) = 3x^2 - 6x + 9 is a hyperbola with asymptotes parallel to the x-axis.

• The graph of the polynomial u(x) = 3x^2 - 6x + 9 is a parabola that opens upwards, narrower than the standard parabola, with the vertex at (1, 6).

• The graph of the polynomial u(x) = 3x^2 - 6x + 9 is a straight line passing through the origin.