Finding the Maximum or Minimum of a Quadratic (3.15.3)

Question 1

• Every parabola has a turning point, or vertex. This point is the minimum point on a positive parabola. It is the
maximum point on a negative parabola.

Answer 1

• Every parabola has a turning point, or vertex. This point is the minimum point on a positive parabola. It is the
maximum point on a negative parabola.

Question 2

• On a parabola opening along the y-axis, the maximum or minimum value relates to the height of the curve. Therefore, it is the k-value of the vertex. This maximum or minimum occurs at the point on the curve when x has the h-value of the vertex.

Answer 2

• On a parabola opening along the y-axis, the maximum or minimum value relates to the height of the curve. Therefore, it is the k-value of the vertex. This maximum or minimum occurs at the point on the curve when x has the h-value of the vertex.

Question 3

This parabola is positive; it will have a minimum.
The minimum value is –1/8 (k). This value occurs at –3/4 (h). Graphing the curve gives us a visual relationship to the changes occurring for various x- and y-values related to this function.

Answer 3

This parabola is positive; it will have a minimum.
The minimum value is –1/8 (k). This value occurs at –3/4 (h). Graphing the curve gives us a visual relationship to the changes occurring for various x- and y-values related to this function.

Question 4

This parabola is a negative curve. So, you know that it will have a maximum point. Doing the arithmetic, you find that the curve’s maximum is 5(k), reached at the point 2(h). Again, a quick sketch of the curve gives you a visual concept of how values change across the span of this curve.

Answer 4

This parabola is a negative curve. So, you know that it will have a maximum point. Doing the arithmetic, you find that the curve’s maximum is 5(k), reached at the point 2(h). Again, a quick sketch of the curve gives you a visual concept of how values change across the span of this curve.