Y 2x 2 3x 1 in vertex form
Asked by maham237 @ in Mathematics viewed by 341 People
Write y = 2x^2 + 8x + 3 in vertex form.
Answered by maham237 @
We'll use "completing the square" to rewrite y = 2x^2 + 8x + 3 in vertex form:
y = 2(x^2 + 4x ) + 3
Halve the coefficient of x (that is, halve 4), obtaining 2, and then square 2.
Add this 2 and then subtract it as shown below:
y = 2(x^2 + 4x + 4 - 4 ) + 3
Next, rewrite x^2 + 4x + 4 as the square of a binomial:
y = 2( (x+2)^2 - 4 ) + 3
Multiply the -4 term by 2 and take the result outside the parentheses:
y = 2( (x+2)^2 ) + 3 - 8
Simplifying this result:
y = 2( (x+2)^2 ) - 5
Thus, the vertex is at x = -2 and y = -5: (-2, -5).
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