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 51 Page 225

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

Minimum Value: - 9.375
Domain: {all real numbers}
Range: {f(x)|f(x)≥ - 9.375}

Practice makes perfect

Let's begin by rewriting our function in the general expression of a quadratic function, f(x)=ax^2+bx+c. f(x) = - 9+3x+6x^2⇔ f(x) = 6x^2 +3x +(- 9) We can see that a = 6, b = 3, and c = - 9.

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=6, 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(6)
â–Ľ
Simplify
- 3/12
- 1/4
Now, we can find the y-coordinate by evaluating the function for x = - 14.
f(x) = - 9+3x+6x^2
f( - 1/4) = - 9 +3( - 1/4)+ 6( - 1/4)^2
â–Ľ
Simplify
f(- 1/4) = - 9+3(- 1/4)+ 6 ( 1/16)
f(- 1/4) = - 9-3/4+6/16
f(- 1/4) = - 9-3/4+3/8
f(- 1/4) = - 9-6/8+3/8
f(- 1/4) = - 72/8-6/8+3/8
f(- 1/4) = - 75/8
f(- 1/4) = - 9.375
The minimum value of our function is - 9.375.

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 - 9.375, the range is all real numbers greater than or equal to - 9.375. Domain:& {all real numbers} Range:& {f(x)|f(x)≥ - 9.375}