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Quad Test 1 Review

Authored by Stephanie Genzer

Mathematics

10th Grade

CCSS covered

Used 56+ times

Quad Test 1 Review
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20 questions

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1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Answer explanation

The equation f(x) = 3 - (x + 3)^2 can be rewritten as f(x) = - (x + 3)^2 + 3, which matches the first answer choice. The negative sign indicates a reflection over the x-axis, maintaining the same vertex.

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Complete the square and write in Vertex Form 
f(x) = x2 + 4x + 9

f(x) = (x+2)2 + 5

f(x) = (x - 2)2 + 5

f(x) = (x+4)2 + 5

f(x) = (x+2)2 - 5

Answer explanation

To complete the square for f(x) = x² + 4x + 9, we rewrite it as f(x) = (x+2)² + 5. The vertex form is f(x) = (x+2)² + 5, confirming the correct choice is f(x) = (x+2)² + 5.

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Answer explanation

To convert to vertex form, we complete the square. Starting with y = 6(x^2 + 2x) + 13, we add and subtract 1 inside the parentheses: y = 6((x+1)^2 - 1) + 13 = 6(x+1)^2 + 7. Thus, the correct answer is y=6(x+1)^2+7.

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What type of parabola is described here: It has a focus of (2, -3) and a directrix of y = 7

A vertical parabola that opens up

A horizontal parabola that opens left

A vertical parabola that opens down

A horizontal parabola that opens right

Answer explanation

The focus (2, -3) is below the directrix y = 7, indicating the parabola opens downwards. Since the focus is below the directrix, it confirms that this is a vertical parabola that opens down.

Tags

CCSS.HSF-IF.C.7A

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Answer explanation

To simplify \( f(x) = \frac{1}{3}(3x-9)^2 + 1 \), factor out \( 3 \) from the expression: \( (3(x-3))^2 = 9(x-3)^2 \). Thus, it becomes \( f(x) = 3(x-3)^2 + 1 \), matching the correct choice.

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

A quadratic function has a vertex of (2, 3) and the point (0, -9) is on the parabola. Which other point must also be on the parabola?

(-9, 0)

(4, -9)

(-2, -9)

(0, -4)

Answer explanation

The vertex (2, 3) indicates symmetry. Since (0, -9) is on the left, the corresponding point on the right is found by reflecting across the vertex, resulting in (4, -9) being on the parabola.

Tags

CCSS.HSF-IF.C.7A

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The graph has a maximum.

The vertex of the function is at (c, d).

The axis of symmetry is at x = c

The focus is on the x-axis.

Answer explanation

The focus of a quadratic function in this form is not on the x-axis; it is located at (c, d + 1/(4a)), which is above the x-axis since a < 0. Thus, the statement 'The focus is on the x-axis' is NOT true.

Tags

CCSS.HSF-IF.C.7A

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