Try these ten multiple-choice questions on parabolas: axis of symmetry, vertex, zeros, intercepts, completing the square and real-world maximums. Each question has exactly one correct answer, and the explanation shows the common mistake.
Algebra 1Common Core: F-IF.C.7a · F-IF.C.8a · F-IF.B.4 · A-SSE.B.3b
🎯 Graphing Quadratic Functions – Algebra 1 math quiz
Question 1
What is the axis of symmetry of \(y=x^{2}-10x+7\)?
A
\(x=-5\)
B
\(x=10\)
C
\(x=7\)
D
\(x=5\)
Question 2
What is the vertex of the parabola shown?Graph for the question.
A
\((-3, 2)\)
B
\((3, 2)\)
C
\((3, -2)\)
D
\((-2, 3)\)
Question 3
What is the vertex of \(y=2(x+4)^{2}-7\)?
A
\((4, -7)\)
B
\((-4, -7)\)
C
\((-4, 7)\)
D
\((4, 7)\)
Question 4
What are the zeros of \(y=(x-6)(x+2)\)?
A
\(x=-6\text{ and }x=2\)
B
\(x=6\text{ and }x=2\)
C
\(x=6\text{ and }x=-2\)
D
\(x=-6\text{ and }x=-2\)
Question 5
What is the y-intercept of \(y=(x-3)(x+4)\)?
A
\((0, -12)\)
B
\((0, 12)\)
C
\((0, -1)\)
D
\((0, 4)\)
Question 6
Which equation matches the graph?Graph for the question.
A
\(y=(x-1)^{2}+4\)
B
\(y=-(x-1)^{2}+4\)
C
\(y=-(x+1)^{2}+4\)
D
\(y=-(x-1)^{2}-4\)
Question 7
Complete the square: \(x^{2}+12x+5\) equals
A
\((x+6)^{2}-31\)
B
\((x+6)^{2}+41\)
C
\((x+6)^{2}+5\)
D
\((x+12)^{2}-139\)
Question 8
What is the minimum value of \(f(x)=x^{2}-8x+19\)?
A
\(4\)
B
\(19\)
C
\(-3\)
D
\(3\)
Question 9
The graph shows the height in feet of a ball after \(t\) seconds. When does the ball return to the ground?Graph for the question.
A
\(t=4\text{ s}\)
B
\(t=2\text{ s}\)
C
\(t=8\text{ s}\)
D
\(t=64\text{ s}\)
Question 10
A rectangular pen has a perimeter of 60 feet. What is the largest area it can have?
A
\(450\text{ ft}^{2}\)
B
\(900\text{ ft}^{2}\)
C
\(200\text{ ft}^{2}\)
D
\(225\text{ ft}^{2}\)
🎉 Quiz complete!
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Remember:
- Standards F-IF.C.7a, F-IF.C.8a, F-IF.B.4 and A-SSE.B.3b: graph quadratics, rewrite them, and interpret key features.
- The axis of symmetry is \(x=-\frac{b}{2a}\), and the vertex lies on it.
- Vertex form \(a(x-h)^{2}+k\) shows the vertex; factored form \(a(x-p)(x-q)\) shows the zeros.
- If \(a > 0\) the vertex is a minimum; if \(a < 0\) it is a maximum.
- In a projectile model, the vertex gives the maximum height and the positive zero gives the landing time.
See every chapter on the Algebra 1 math page.