Select the correct vertex form of the following equation. y=x2+6x−9 (1 point) Responses y=(x−3)2−18 y is equal to open paren x minus 3 close paren squared minus 18 y=(x+3)2+32 y is equal to open paren x plus 3 close paren squared plus 32 y=(x−3)2−4 y is equal to open paren x minus 3 close paren squared minus 4
The correct vertex form of the equation y=x^2+6x-9 is y=(x+3)^2-18.
To find the vertex form of the given equation y = x^2 + 6x - 9, we need to complete the square.
Step 1: Group the x terms together:
y = (x^2 + 6x) - 9
Step 2: Take half of the coefficient of the x term and square it:
Half of 6 is 3, and 3 squared is 9.
Step 3: Add the value obtained in step 2 inside the parentheses and subtract it outside the parentheses:
y = (x^2 + 6x + 9) - 9 - 9
Step 4: Simplify the equation:
y = (x + 3)^2 - 18
Therefore, the correct vertex form of the equation y = x^2 + 6x - 9 is y = (x + 3)^2 - 18, which corresponds to the response "y=(x+3)2-18"
To determine the correct vertex form of the given quadratic equation, y = x^2 + 6x - 9, we need to complete the square by following these steps:
Step 1: Write the equation in the form y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
Step 2: Group the terms involving x^2 and x, and leave the constant term separately.
y = (x^2 + 6x) - 9
Step 3: Complete the square for the terms involving x. Take half of the coefficient of x, square it, and add it to both sides of the equation.
y = (x^2 + 6x + 9) - 9 - 9
Step 4: Factor the perfect square trinomial in the parentheses and simplify.
y = (x + 3)^2 - 18
Based on the above steps, the correct vertex form of the equation y = x^2 + 6x - 9 is:
y = (x + 3)^2 - 18
Therefore, the correct response is: y = (x + 3)^2 - 18.