Quad Test 1 Review

Quiz
•
Mathematics
•
10th Grade
•
Easy
Standards-aligned
Stephanie Genzer
Used 54+ times
FREE Resource
14 questions
Show all answers
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
Find the vertex, focus, and directrix of the parabola: x2 = 28y
Vertex: (0, 0) Focus: (0,7) Directrix: y=-7
Vertex: (0, 0) Focus: (7,0) Directrix: y=7
Vertex: (0, 0) Focus: (0,-7) Directrix: x=-7
Vertex: (0, 0) Focus: (7, 0) Directrix: x=7
Answer explanation
The equation x^2 = 28y represents a parabola that opens upwards. The vertex is at (0, 0). The focus is at (0, 7) and the directrix is y = -7, which matches the correct answer choice.
5.
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
6.
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.
7.
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
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