Convert from standard to vertex form:
(x+5)(x+4)
x^2+ 9x + 20
(x+3)^2 + 20 - 9
(x+3)^2 + 11 <------
not quite. since (x+a)^2 = x^2+2ax+a^2,
x^2+9x = x^2+9x+(9/2)^2-(9/2)^2
x^2+9x+20
= (x + 9/2)^2 + 20-81/4
= (x + 9/2)^2 + 319/4
One question:
Shouldn't the answer be (x + 9/2)^2 -1/4 ?
Because 20 - (81/4) = -0.25
I agree with you
x^2+9x+20
= x^2 + 9x + 81/4 - 81/4 + 20
= (x+9/2) + 20 - 81/4
= (x+9/2)^ - 1/4
Thank you!
To convert from standard form to vertex form, you need to complete the square. Here's how you can do it:
1. Expand the given equation: (x + 5)(x + 4)
This gives you: x^2 + 4x + 5x + 20
2. Combine like terms: x^2 + (4x + 5x) + 20
Simplify further: x^2 + 9x + 20
3. Write the equation in the form (x - h)^2 + k, where (h, k) represents the vertex.
To complete the square, take half of the coefficient of x (which is 9) and square it:
(9/2)^2 = 81/4
4. Add and subtract the value obtained in the previous step to the equation from step 2:
x^2 + 9x + 81/4 - 81/4 + 20
5. Group the first three terms and simplify:
(x^2 + 9x + 81/4) - 81/4 + 20
(x + 9/2)^2 - 81/4 + 80/4
6. Simplify further:
(x + 9/2)^2 - 1/4
So, the equation in vertex form is (x + 9/2)^2 - 1/4, and the vertex is at (-9/2, -1/4).