Question 524448: Given the function f(x)=-2(x+5)^2+10 complete the following. Please show all of your work.
i. If f(x)=10, what is x ?
ii. What point(s) from part (i) are on the graph of f?
iii. List the x-intercepts, if any, of the graph of f.
iv. List the y-intercept, if there is one, of the graph of f.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Given the function f(x)=-2(x+5)^2+10 complete the following. Please show all of your work.
i. If f(x)=10, what is x ?
ii. What point(s) from part (i) are on the graph of f?
iii. List the x-intercepts, if any, of the graph of f.
iv. List the y-intercept, if there is one, of the graph of f.
**
i. f(x)=-2(x+5)^2+10
10=-2(x+5)^2+10
-2(x+5)^2=0
(x+5)^2=0
(x+5)(x+5)=0
x=-5 (muliplicity 2)
..
II. (-5,0) is on the graph of f twice.
..
III. x-intercepts
set y=0
0=-2(x+5)^2+10
0=2(x^2+10x+25)+10
0=2x^2+20x+50+10
2x^2+20x+60=0
x^2+10x+30=0
(discriminant)=b^2-4ac=10^2-4*1*30=100-120=-20
Therefore, no real solutions (no x-intercepts)
..
iv. y-intercept
set x=0
f(x)=-2(x+5)^2+10
y=-2(x+5)^2+10
y=-2(5^2)+10
y=-50+10=-40
y-intercept=-40
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