Question

Use completing the square to describe the graph of the following function, support your answer graphically.

f(x)=-2x^2+4x+5

Answer 1

f=-2(x^2+2x+5/2)
=-2(x^2+2x+1+3/2)
=-2(x^2+2x+1)-2*3/2
=-2(x+1)^2-3

Answer 2

@greenlegodude57 can you help? im not sure what that guy did =(

Answer 3

I'm not sure about this one, sorry.

@gorv Could you explain to her?

Answer 4

ok thanks @greenlegodude57

Answer 5

we need to make perfect square @jdorta1

Answer 6

r u there ??

Answer 7

im horrible at this stuff, so if you can explain how to do it =(

Answer 8

yes

Answer 9

x^2 is there so make a a perfect square using this

Answer 10

x^2+2*a*x+a^2=(x+a)^2

Answer 11

take -2 c0mmon

Answer 12

I'm bad at the "perfect square" thing too.

Answer 13

ok

Answer 14

The problem wants you to find the zeroes by "completing the square"
f(x)= -2x^2 + 4x +5 = 0
First step get the coefficient of the "x^2" term to equal a 1. To do this we divide the equation by -2 (both sides)
x^2 - 2x -5/2 = 0 (0 divided by -2 is still 0)
Next step as 5/2 to both sides in order to get the constant on the right hand side.
x^2 -2x = 0 +5/2
Now divide the coefficient of the x term by 2 (taking half of it), then square it and add it to both sides of the equation
x^2 -2x + 1 = 5/2 + 1. Now on the left side you have the perfect square, express it so.
(x - 1)^2 = 7/2 (adding the right hand side.
Do you follow the steps so far? Because the finale is near.

Answer 15

The final step is to take the square root of both sides and solve for x.

Answer 16

\[\sqrt{(x - 1)2}=\sqrt{7/2}\]\[x - 1 =\sqrt{7/2}\]\[x = 1\pm \sqrt{7/2}\]The radical can be further simplified. Do you know how to "rationalize" the denominator?