Algebra 1 Practice Test: Graphing Quadratic Functions
- Graphing Quadratic Functions
- 10 questions
- 13 minutes
These 10 questions are about the parabola y = ax² + bx + c. The axis of symmetry is x = −b/(2a), and the sign of a tells you whether the parabola opens up or down.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
Your result
- 0 correct
- 0 wrong
- 0 blank
-
Question 1
What is the vertex of y = (x − 3)2 + 2?
Correct answer: B
In vertex form y = a(x − h)2 + k the vertex is (h, k). Since x − 3 means h = 3, the vertex is (3, 2), not (−3, 2).
-
Question 2
What is the axis of symmetry of y = 2x2 − 8x + 1?
Correct answer: D
Use x = −b2a = −−82 · 2 = 2. Forgetting the factor 2 in the denominator gives 4.
-
Question 3
What is the vertex of y = x2 + 6x + 5?
Correct answer: A
The vertex has x = −62 = −3, and y = 9 − 18 + 5 = −4. Using x = 3 comes from dropping the minus sign in −b2a.
-
Question 4
Which statement is true about y = −2(x + 1)2 + 5?
Correct answer: C
Since a = −2 is negative, the parabola opens down and its vertex (−1, 5) is the highest point. So the maximum value is the y-coordinate, 5.
-
Question 5
What is the y-intercept of y = 3x2 − 4x − 7?
Correct answer: B
At the y-intercept x = 0, so y = 0 − 0 − 7 = −7. The y-intercept of a quadratic in standard form is always c.
-
Question 6
What are the x-intercepts of y = x2 − 2x − 8?
Correct answer: D
Set y = 0: (x − 4)(x + 2) = 0, so x = 4 or x = −2. Reading the numbers from the factors without changing the signs gives −4 and 2.
-
Question 7
How is the graph of y = −x2 + 4 related to the graph of y = x2?
Correct answer: A
The negative sign in front of x2 reflects the graph over the x-axis, and +4 moves it up 4 units. The width does not change because |a| = 1.
-
Question 8
What is the range of y = (x − 1)2 − 3?
Correct answer: C
The parabola opens up and its lowest point is the vertex (1, −3), so every y-value is at least −3. The value 1 is the x-coordinate of the vertex, not a y-value bound.
-
Question 9
Which is the vertex form of y = x2 − 4x + 7?
Correct answer: B
Complete the square: x2 − 4x + 4 + 3 = (x − 2)2 + 3. Keeping +7 forgets to subtract the 4 that was added.
-
Question 10
A parabola has vertex (1, −8) and passes through (3, 0). Which equation describes it?
Correct answer: A
Start with y = a(x − 1)2 − 8 and substitute (3, 0): 0 = 4a − 8, so a = 2. (x + 1) would put the vertex at x = −1.
Questions you leave blank are not counted as wrong.
More Math tests
MathAlgebra 1 Practice Test: Simplifying RadicalsSimplifying Radicals10 questions13 min MathAlgebra 1 Practice Test: Solving Linear Equations and InequalitiesSolving Linear Equations and Inequalities15 questions20 minMathAlgebra 1 Practice Test: Linear Functions, Slope and GraphsLinear Functions, Slope and Graphs15 questions20 minMathAlgebra 1 Practice Test: Systems of Equations and InequalitiesSystems of Equations and Inequalities15 questions20 minMathAlgebra 1 Practice Test: Exponents, Polynomials and FactoringExponents, Polynomials and Factoring15 questions20 minMathAlgebra 1 Practice Test: Quadratic Equations and FunctionsQuadratic Equations and Functions15 questions20 minMathAlgebra 1 Practice Test: Literal EquationsLiteral Equations10 questions13 min