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 9 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: - 13
Domain: {all real numbers}
Range: {f(x)|f(x)≥ - 13}

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) = 3x^2+8x+5⇔ f(x) = 3x^2 + 8x + 5 We can see that a = 3, b = 8, and c = 5.

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=3, 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
- 8/2(3)
- 8/6
- 4/3
Now, we can find the y-coordinate by evaluating the function for x = - 43.
f(x) = 3x^2 + 8x +5
f ( - 4/3 ) = 3( - 4/3 )^2 + 8 ( - 4/3 ) +5
â–Ľ
Simplify right-hand side
f(- 4/3 ) = 3 ( 16/9 )+ 8 (- 4/3 )+5
f(- 4/3 ) = 3 * 16/9 + 8 (- 4/3 )+5
f(- 4/3 ) = 48/9 + 8 (- 4/3 )+5
f(- 4/3 ) = 16/3 + 8 (- 4/3 )+5
f(- 4/3 ) = 16/3 -32/3+5
f(- 4/3 ) = 16/3 -32/3+15/3
f(- 4/3 ) = - 1/3
The minimum value of our function is - 13.

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 - 13, the range is all real numbers greater than or equal to - 13. Domain:& {All real numbers} Range:& {f(x)|f(x)≥ - 13}