(-2, 5) Minimum
Step-by-step explanation:
y-5=(1/3)(x + 2)²
y-5=(1/3)(x²+4x+4))
y-5=1/3x²+4/3x+4/3
y=1/3x²+4/3x+4/3+5
y=1/3x²+4/3x+4/3+15/3
y=1/3x²+4/3x+19/3
graph is attached
x= -b/2a
x= (-4/3)/2(1/3)
x= (-4/3)/(2/3)
x= (-4/3)*(3/2)
3's cancel
x= (-4/1)*(1/2)
x = -4/2
x = -2
plug -2 back into
y=1/3x²+4/3x+19/3
y=1/3*4+4/3*-2+19/3
y=4/3-8/3+19/3
y=15/3
y=5
(-2,5)
if a is positive
graph looks like a smile
so minimum
if a is negative
graph looks like a frown
so maximum
quadraticswbi.weebly.com
Answer:
x+12
Step-by-step explanation:
Problem 1 (on the left)
It appears we have an exponential function curve through the points (0,4) and (1,7)
The general exponential function is of the form
y = a*b^x
The value of 'a' is the y intercept or initial value. So a = 4
Plug in (x,y) = (1,7) to help solve for b
y = a*b^x
y = 4*b^x
7 = 4*b^1
7 = 4b
b = 7/4 = 1.75
Therefore, the function is y = 4*(1.75)^x
- Plug in x = 0 and you should get y = 4.
- Plug in x = 1 and you should get y = 7
These two facts help confirm we have the correct exponential equation.
<h3>Answer: y = 4*(1.75)^x</h3>
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Problem 2 (on the right)
The steps will follow the same idea as the previous question.
The exponential curve goes through (-1, 120) and (0,40)
We have a = 40 this time due to the y intercept (0,40)
Plug in the coordinates of the other point to find b
y = a*b^x
y = 40*b^x
120 = 40*b^(-1)
120 = 40/b
120b = 40
b = 40/120
b = 1/3
<h3>Answer: y = 40*(1/3)^x</h3>
