1. Determine the form of the following quadratic equation, and identify the values for the key characteristic of the parabola revealed by that form. f(x)=(2x−1)(x+6) (1 point) A. The equation is in standard form. The key characteristic is the location of the y-intercept, (0, −6). B. The equation is in factored form. The key characteristic is the location of the y-intercept, (0, −6). C. The equation is in standard form. The key characteristic is the location of the x-intercepts, (1/2,0) and (−6,0). D. The equation is in factored form. The key characteristic is the location of the x-intercepts, (1/2,0) and (−6,0). 2. Convert the following equation into both intercept form and standard form.

f(x)=1/4(x+4)^2−9

(1 point)

intercept form f(x)=(x+10)(x−2); standard form f(x)=x^2+8x−20

intercept form f(x)=(1/2x+9)(1/2x−1); standard form f(x)=1/4x^2+4x−9

intercept form f(x)=(1/2x+3)(1/2x−3); standard form f(x)=14x^2−9

intercept form f(x)=(1/2x+5)(1/2x−1); standard form f(x)=1/4x^2+2x−5

3. Chris is asked to graph the quadratic function f(x)=(x+4)^2−1. He recognizes that the graph is in vertex form, so he first plots the vertex (−1,−4). Then he finds a point to the left of the vertex, (−3,0), by substituting x=−3 into the equation. He then reflects this point over the axis of symmetry, x=−1, to obtain the point (1,0). He then connects the points with a smooth curve to obtain the graph below. Did Chris correctly graph the quadratic function? If not, what error did he make?

A function is graphed on a four quadrant coordinate plane. The x-axis and the y-axis go from negative 10 to 10 in increments of 1. A U-shaped curve that opens upward has a vertex at left parenthesis negative 1 comma negative 4 right parenthesis, and passes through left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 1 comma 0 right parenthesis.

(1 point)

A. Chris plotted the vertex incorrectly. He reversed the x- and y-coordinates.

B. Chris did not reflect the point (−3,0) correctly. He should have reflected across x=0.

C. Chris did not identify the form of the equation correctly. He should have recognized that the equation is in standard form, so he should have started by plotting the y-intercept, and then factored to find the zeros.
D. Chris correctly graphed the quadratic function.

4. The following equations represent the same quadratic function written in standard, vertex, and intercept form, respectively.

f(x)=0.5x2+x−1.5, f(x)=0.5(x+1)2−2, f(x)=(0.5x+1.5)(x−1)

Based on these equations, which of the following is a trait of the graph of f(x)?

(1 point)

A. The line of symmetry is x=0.5.

B. The graph falls toward negative infinity to both the left and the right.

C. The range is y ≥ -2.

D. The y-intercept is (0, -2).