Answer:
Step-by-step explanation:
Please use " ^ " to indicate exponentation: y= x^2 + 11x + 24. Thanks.
Because x^2 is positive, the graph of this parabola opens up.
We can find the vertex and roots (zeros) as follows, using the quadratic formula:
With a = 1, b = 11 and c = 24,
-11 ± √ [ (11^2-4(1)(24) ] -11 ± √25
x = ------------------------------------ = --------------- = -3 and x = -8
2(1) 2
This tells us that the x-intercepts are at (-3, 0) and (-8, 0). The minimum value is at x = -b / (2a), which here is x = -11 / [2] = -5 1/2 (which is halfway between the zeros).
The vertex (and thus, the minimum) is at (-5 1/2, f(-5 1/2) ).
Answer:
f(9) = 24
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 4(x - 3)
f(9) is x = 9
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>: f(9) = 4(9 - 3)
- Subtract: f(9) = 4(6)
- Multiply: f(9) = 24
3-4=-1. To use mental math, imagine that there is a number line in your head. Start at three, and since we're subtracting, move to the left 4 units. This will land you at -1. I hope this gets easier for you in the future!
Range: difference between the highest and lowest values
First order from smallest to greatest
3, 8, 24, 24, 29, 38, 62
Smallest number: 3
Largest number: 62
62 - 3 = 59
Solution: the range is 59
