Algebra 1 Graphing Quadratic Functions and Transformations Test Solutions and Scoring (PDF)

\(a = 2, h = 3, k = -1\).

Vertex \((3, -1)\); axis \(x = 3\); opens up

Scoring: 1 point for the vertex and axis; 1 point for the direction.

\(x = -\frac{-10}{2(1)} = 5\). Then \(y = 25 – 50 + 16 = -9\).

\((5, -9)\)

Scoring: 1 point for the x-coordinate; 1 point for the y-coordinate.

y-intercept: \((0, -6)\). Factor: \((x – 3)(x + 2) = 0\).

(0, -6); (3, 0) and (-2, 0)

Scoring: 1 point for the y-intercept; 1 point for both x-intercepts.

Axis \(x = 1\). Vertex \((1, -4)\). Intercepts \((-1, 0)\), \((3, 0)\), \((0, -3)\).

Scoring: 1 point for the correct vertex; 1 point for a correct smooth graph.

Left 3 (from \(x + 3\)), reflection over the x-axis (the negative sign), and up 2.

Left 3, reflect, up 2

Scoring: 1 point for the shifts; 1 point for the reflection.

\(y = (x^{2} + 4x + 4) – 4 + 1\).

\(y = (x + 2)^{2} – 3\)

Scoring: 1 point for adding and subtracting 4; 1 point for the vertex form.

a) \(t = -\frac{32}{2(-16)} = 1\).

b) \(h(1) = -16 + 32 + 6 = 22\).

c) \(h(0) = 6\).

1 second; 22 feet; 6 feet

Scoring: 1 point per part.

a) \(A = x(30 – x) = -x^{2} + 30x\).

b) \(x = -\frac{30}{2(-1)} = 15\).

c) \(A(15) = 15 \cdot 15 = 225\).

225 square feet when x = 15

Scoring: 1 point per part.

The minimum of \(f\) is 5. For \(g\): \(x = 3\), \(g(3) = 9 – 18 + 12 = 3\).

\(f\) has the greater minimum (5 versus 3)

Scoring: 1 point for each minimum value.