Vertex Form

Show your work for each problem.

1.
What is the vertex of ?
1. a)
2. b)
3. c)
4. d)
Answer:
From , we have and . The vertex is .
2.
What is the vertex of ?
1. a)
2. b)
3. c)
4. d)
Answer:
, so . With , the vertex is .
3.
Which direction does the parabola open?
1. a)Downward
2. b)Upward
3. c)Right
4. d)Left
Answer: Downward
Since , the parabola opens downward. The vertex is the maximum point.
4.
What is the x-coordinate of the vertex of ?
Answer: 7
From , we see that . The x-coordinate of the vertex is .
5.
What is the y-coordinate of the vertex of ?
Answer: -9
The constant is the y-coordinate of the vertex. The vertex is .
6.
What is the axis of symmetry of ?
1. a)
2. b)
3. c)
4. d)
Answer:
, so . The axis of symmetry is .
7.
The vertex of is a:
1. a)Minimum point
2. b)Origin
3. c)Maximum point
4. d)Inflection point
Answer: Maximum point
Since , the parabola opens downward. The vertex is the highest point, a maximum.
8.
What is the value of in if the parabola passes through ?
Answer: 2
9.
A ball's height is meters. What is the maximum height?
Answer: 45
The vertex is . Since , this is a maximum. The maximum height is meters.
10.
Find the vertex and axis of symmetry of
Answer: (-2, -8), x = -2
1. Identify the value of : 2
2. Find (remember ): -2
3. Find : -8
4. Write the axis of symmetry (just the number): -2
11.
Write the equation in vertex form for a parabola with vertex that opens upward with
Answer: y = 3(x - 4)^2 - 2
1. What is ? 4
2. What is ? -2
3. What goes inside the parentheses: ? 4
4. What is the final value added/subtracted? -2
12.
Write the vertex form equation for a parabola with vertex passing through
Answer: y = 2(x + 1)^2 + 5
1. Start with the partial equation using the vertex. What is ? (x + 1)
2. The partial equation is . Substitute : what is ? 4
3. Now solve for : 2
4. Write the final value of : 2
13.
A company's profit is euros where is the price. What price maximizes profit?
Answer: 30
The vertex is at . Since , this is a maximum. The optimal price is 30 euros.
14.
For , at what x-values does the parabola cross the x-axis? Give the smaller value.
Answer: 0
or . The smaller is .
15.
A fountain's water arc follows meters. Find the maximum height and where the water lands (x-intercepts).
Answer: 8 meters, x = 0 and x = 8
1. What is the maximum height (the k value)? 8
2. At what x-value is the maximum height reached? 4
3. To find where water lands, solve . What is ? 16
4. If , what are the two x values? (smaller first) 0, 8
16.
Which equation represents a parabola that opens downward with vertex at ?
1. a)
2. b)
3. c)
4. d)
Answer:
Vertex means and . So we need and . For downward, must be negative. Answer: