How can I find the x-intercepts for this equation?

Question

f(x) = -.5 (x+2) ^2 + 4.5

I found the vertex which is (-2, 4.5). I also found the y-intercept which is (0, 2.5).

Sorry if this is a stupid question.

Do I facor out the (x+2)^2

Answer 1

LOl Darling of course its not stupid . We cant know everything , Its Haman's nature

well dear Jazz

■ Step 1
-0.5 (x+2) ^2 + 4.5=0
if you find the roots , the roots will be x-intercepts
x1 = -5 & x2 = 1
x-intercepts are ( -5 , 0 ) & ( 1 , 0 )
( x-intercept is where y = 0 )

■ Step 2
y-intercept is where x = 0
y = -0.5 (x+2) ^2 + 4.5
y = -0.5 ( 0 +2 ) ^ 2 + 4.5
y = 2.5
y-intercept is ( 0 , 2.5 )

Good Luck Darling ♣
{ well dear if you have probelm with this part (x+2) ^2 i will explain it for you ;
( a + b ) ^ 2 = a ^2 + b ^2 + 2ab so ;
(x+2) ^2 = x^2 + 2x + 4
-0.5 ( x^2 + 2x + 4 ) = -0.5 x^2 - 1x - 2
-0.5 x^2 - 1x - 2 + 4.5 = -0.5x^2 - x + 2.5
if a = -0.5 , b = -1 & c = +2.5
Now just find " ∆ = b ^ - 4ac" & " x = - b ± √ ∆ / 2a " } ....

Answer 2

At an x intercept f(x) = 0

So -0.5(x+2)^2 + 4.5=0

-0.5(x+2)^2 =-4.5

(x+2)^2 =9

then expand (x+2)^2 giving:

x^2 + 4x + 4 = 9

x^2 + 4x -5 = 0

Now we need to factorise this and solve for x

factorising:

(x-1)(x+5)=0

Hence x-1=0, x+5=0 giving x=1 or x=-5

You can verify this by subbing in the values of x into the original eqn and it will equal 0

Answer 3

x=3/2 and x= -1

Answer 4

X-intercepts occur when y=0. If you set y=0, subtract 4.5 from both sides, and then multiply by -2, you have 9=(x+2)^2. Remember that when you take the square root of something, there is a positive and negative answer. Take the square root of both sides and re-arrange for x (remember that sqrt(9) = +/- 3)

Answer 5

To find the x-intercepts set f(x) equal to zero. Then solve for x.

0 = -.5(x+2)^2 + 4.5

Hope this helps. And it's not a stupid question if you are not sure what to do.

Answer 6

Not a stupid question. The x-intercept is where f(x)=0, so you then need to find the roots of the quadratic equation, which can be done sometimes by inspection, but often requires completing the square, or using the quadratic formula, which is the result of completing the square.

Answer 7

The x-intercepts are -5 and 1. To solve this equation you could of course graph it.

Answer 8

where y=0 [or f(x)=0]

therefore,
0=-0.5[x+2]^2+4.5
-4.5=-1/2[x+2]^2
9=[x+2]^2 square root it
3=x+2
x=1 <- therefore x-intercept (1,0)