McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
1. Graphing Quadratic Functions
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Exercise 8 Page 224

Identify a, b, and c in the given quadratic function. What does the value of a tell you about the function?

Minimum Value: - 14.25
Domain: {all real numbers}
Range: {f(x)|f(x)≥ - 14.25}

Practice makes perfect

Let's begin by rewriting our function in the general expression of a quadratic function, y=ax^2+bx+c. f(x) = x^2+3x-12⇔ f(x) = 1x^2 + 3x + (- 12) We can see that a = 1, b = 3, and c = - 12.

Determining Maximum or Minimum Value

Before we determine the maximum or minimum recall that, if a>0, the parabola has a minimum value. Conversely, if a<0, the parabola has a maximum value.

In the given function, we have a=1, which is greater than 0. Thus, the parabola will have a minimum value.

Finding the Maximum or Minimum Value

The minimum or maximum value of a parabola is always the y-coordinate of the vertex. We can find it by first looking for the x-coordinate of the vertex, - b2a.
- b/2a
- 3/2(1)
- 3/2
Now, we can find the y-coordinate by evaluating the function for x = - 32.
f(x) = x^2 + 3x -12
f ( - 3/2 ) = ( - 3/2 )^2 + 3 ( - 3/2 ) - 12
â–Ľ
Simplify
f(- 3/2 ) = 9/4 + 3 (- 3/2 )- 12
f(- 3/2 ) = 9/4-9/2-12
f(- 3/2 ) = 9/4-18/4-12
f(- 3/2 ) = 9/4-18/4-48/4
f(- 3/2 ) = 9-18-48/4
f(- 3/2 ) = - 57/4
f(- 3/2 ) = - 57/4
f(- 3/2 ) = - 14.25
The minimum value of our function is - 14.25.

Domain and Range

Unless there is a specific restriction given in the context of the problem, the domain of a quadratic function is all real numbers. In this case, there is no restriction on the value of x. Since the minimum value of the function is - 14.25, the range is all real numbers greater than or equal to - 14.25. Domain:& {All real numbers} Range:& {f(x)|f(x)≥ - 14.25}