Which of the following best describes the vertex for the function y = -2x2 – 6x + 3?

A. The vertex is (7.5, -1.5) and -1.5 is the maximum value.
Incorrect. Write all order pairs as (x, y).

B. The vertex is (-1.5, 7.5) and 7.5 is the minimum value.
Incorrect. The coefficient of x squared determines if the vertex has the minimum or maximum value.

C. The vertex is (-1.5, 7.5) and 7.5 is the maximum value.
Correct! You identified the vertex point and maximum value.

D. The vertex is (0, 3) and 3 is the minimum value.
Incorrect. The y-coordinate of the vertex is the maximum or minimum value.

What is the vertex and axis of symmetry of the parabola y = x2 − 14x + 48?

  1. Vertex: (7, -1); axis of symmetry: x = 7
  2. Vertex: (7, 1); axis of symmetry: x = 7
  3. Vertex: (-7, -1); axis of symmetry: x = -7
  4. Vertex: (7, -1); axis of symmetry: x = -1

A
Correct! You identified the vertex and axis of symmetry.

B
Incorrect. If point is below the x-axis, the y-coordinate is negative.

C
Incorrect. If point is to the right of the y-axis, the x-coordinate is positive.

D
Incorrect. Axis of symmetry goes through the vertex.

Which equation describes a parabola with a vertex of (2, 4) and has the y-intercept at the origin?

  1. y = (x + 2)2 + 4
  2. y = -(x − 4)2 + 2
  3. y = (x − 2)2 + 4
  4. y = -(x − 2)2 + 4

A
Incorrect. Careful. The x-value of the vertex for (x + h) is -h.

B
Incorrect. Remember that the x-coordinate of the vertex comes from the (x – h).

C
Incorrect. This question is asking for a y-intercept at (0, 0).

D
Correct! You used the vertex and y-intercept.

The graph of y = (x − 5)2 + k is a parabola. Which of the following is true about the value of k?

  1. k is the y-intercept
  2. k is the y-coordinate of the vertex
  3. The opposite of k is the y-coordinate of the vertex
  4. k is the x-coordinate of the vertex

A
Incorrect. Substitute 0 for x to get y-intercept.

B
Correct! The k value is the y-coordinate of the vertex.

C
Incorrect. The “+” sign in front of k does not indicate opposite.

D
Incorrect. The 5 in the parenthesis tells us about the x-coordinate.