Answer: 7) Max: y = 52
8) Min: y = -51
<u>Step-by-step explanation:</u>
The Max/Min is the y-value of the intercept.
- Max is when the a-value is negative.
- Min is when the a-value is positive.
First, find the x-value of the vertex using the Axis of Symmetry formula:
x = -b/2a. Then plug the x-value into the equation to find the y-value.
7) y = -2x² - 16x + 20
↓ ↓ ↓
a= -2 b= -16 c=20
Max: y = -2(-4)² - 16(-4) + 20
= -2(16) + 64 + 20
= -32 + 84
= 52
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7) y = x² + 12x - 15
↓ ↓ ↓
a= 1 b= 12 c= -15
Max: y = (-6)² + 12(-6) - 15
= 36 - 72 - 15
= 36 - 87
= -51
Answer:
n = -5
Step-by-step explanation:
Answer:
n squared + 3n + 1
Step-by-step explanation:
5,11,19,29
Firstly look at the difference between each number. The first difference is 6 then 8 then 10 etc. After that you look at your created sequence - 6,8,10 etc. The difference is 2 each time. Then applying rules, you have to do the constant difference divided by 2 to get a coefficient of n squared. So in this case it's n squared because 2/2 = 1 so you don't have to place a 1 in front of the n squared. After you create a sequence from the n squared. That would be 1,4,9 etc. Then you need to see how to get from the sequence: 1,4,9 etc to your original sequence: 5,11,19 etc. So if you calculate it you will get 4,7,10 because firstly 5-1 = 4 then 11-4 = 7 etc. The sequence 4,7,10 is a linear sequence so the constant difference is 3 each time. So to get a nth term of a linear sequence you will start off as 3n then you will substitute 1 then 2 then 3 into the 3n. Therefore that would be 3,6 etc. So if you take the first substituted term, that would be 3 as said before then you will have to see how to get from the 3 to 4 so that is just adding 1. So the nth term of this linear sequence is 3n + 1. Check if it works at the end. So the overall nth term of the quadratic sequence is n squared as said before + 3n + 1.
