Question
What is the vertex form of the equation?
y = x2 + 4x – 3
(1 point)
Responses
y = (x – 2)2 – 7
y = ( x – 2) 2 – 7
y = (x + 2)2 – 7
y = ( x + 2) 2 – 7
y = (x – 2)2 + 7
y = ( x – 2) 2 + 7
y = (x + 2)2 + 7
y = ( x + 2) 2 + 7
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The correct vertex form of the equation y = x^2 + 4x - 3 is y = (x + 2)^2 - 7.
To find the vertex form of the equation, we need to complete the square.
Step 1: Group the x-terms and isolate the constant term on one side of the equation:
y = x^2 + 4x – 3
= (x^2 + 4x) – 3
Step 2: Complete the square for the x-terms by taking half of the coefficient of x (which is 4) and squaring it:
= (x^2 + 4x + (4/2)^2) – 3 – (4/2)^2
= (x^2 + 4x + 4) – 3 – 4
= (x + 2)^2 – 7
The vertex form of the equation is:
y = (x + 2)^2 – 7
So the correct response is:
y = (x + 2)2 – 7
To find the vertex form of the equation y = x^2 + 4x - 3, we need to complete the square.
Step 1: Group the x^2 and x terms together.
y = (x^2 + 4x) - 3
Step 2: Take half of the coefficient of x (which is 4), square it, and add it inside the parentheses (and subtract it outside the parentheses) to keep the equation balanced.
y = (x^2 + 4x + 4) - 3 - 4
Step 3: Simplify the equation.
y = (x + 2)^2 - 7
So, the vertex form of the equation y = x^2 + 4x - 3 is y = (x + 2)^2 - 7.
Therefore, the correct response is:
y = (x + 2)2 – 7