To write the given equation in vertex form, which is in the form of "y = a(x - h)^2 + k", we need to complete the square.
Step 1: Rewrite the equation in the form of "y = ax^2 + bx + c" by moving the constant term to the right side:
y + 7 = -x^2 + 6x
Step 2: To complete the square, add the square of half the coefficient of the x-term to both sides of the equation:
y + 7 + (6/2)^2 = -x^2 + 6x + (6/2)^2
y + 7 + 9 = -x^2 + 6x + 9
y + 16 = -(x^2 - 6x + 9)
Step 3: Factor the quadratic on the right side:
y + 16 = -(x - 3)^2
Step 4: Move the constant term to the right side:
y = -(x - 3)^2 - 16
Therefore, the vertex form of the equation y = -x^2 + 6x - 7 is y = -(x - 3)^2 - 16.
what is the vertex form of the equation
y=-x^2+6x-7
show all the steps
1 answer
3 answers