Question

The equation 4x^2+8x+15=0 is being rewritten in vertex form

Answer 1

To rewrite the equation in vertex form, complete the square by dividing the coefficient of x by 2 and squaring it. Then, add and subtract the value obtained within the equation. Finally, rearrange the equation to the vertex form.

Step-by-step explanation:

The given equation 4
`x^2` + 8x + 15 = 0 can be rewritten in vertex form. To do this, we need to complete the square.

Step 1: Divide the coefficient of x by 2 and square it. In this case,
`(8/2)^2` = 16.

Step 2: Add and subtract the value obtained in step 1 within the equation.
`4x^2` + 8x + 16 - 16 + 15 = 0.

Step 3: Rearrange the equation as
`(2x + 4)^2` - 1 = 0.

Therefore, the equation 4
`x^2` + 8x + 15 = 0 can be rewritten in vertex form as
`(2x + 4)^2` - 1 = 0.