Complete the square to identify the vertex of y = x^2 – 16x + 14.
• (8,78)
• (8,30)
• (8,14)
• (8,-50)
To complete the square, we need to rewrite the equation in the form y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.
Given equation: y = x^2 - 16x + 14
First, we take the coefficient of x and divide it by 2, and then square the result:
(-16/2)^2 = 64.
Now, we add and subtract this value inside the parentheses to complete the square:
y = (x^2 - 16x + 64 - 64) + 14
= (x^2 - 16x + 64) - 64 + 14
= (x - 8)^2 - 50
So, the vertex of the parabola is (h,k) = (8,-50).
Therefore, the correct answer is: (8,-50)
To complete the square and identify the vertex of the quadratic equation y = x^2 – 16x + 14, follow these steps:
Step 1: Group the x^2 and x terms together, leaving the constant term separate:
y = (x^2 – 16x) + 14
Step 2: Take half of the coefficient of the x term (in this case, -16) and square it:
(-16/2)^2 = (-8)^2 = 64
Step 3: Add the value obtained in step 2 as a constant term inside the parentheses, and subtract it outside of the parentheses in order to maintain the equation's balance:
y = (x^2 – 16x + 64) - 64 + 14
y = (x^2 – 16x + 64) - 50
Step 4: Factor the trinomial inside the parentheses from step 3:
y = (x - 8)^2 - 50
Now we can see that the equation is in vertex form, y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
Comparing the equation with the vertex form, we find:
h = 8
k = -50
Therefore, the vertex of the parabola y = x^2 – 16x + 14 is (8, -50).
The correct option is (8, -50).
To complete the square and identify the vertex of the quadratic function y = x^2 – 16x + 14, follow these steps:
Step 1: Divide the coefficient of x by 2 and square it.
In this case, the coefficient of x is -16.
(-16 / 2)^2 = (-8)^2 = 64
Step 2: Add and subtract the value obtained in Step 1 within the expression.
y = x^2 – 16x + 14
= (x^2 – 16x + 64) - 64 + 14
Step 3: Rearrange the expression inside parentheses as the square of a binomial.
y = (x – 8)^2 - 50
Now the equation is in vertex form, y = (x – h)^2 + k, where (h, k) represents the vertex.
Comparing the equation to the vertex form, you can see that the vertex is (h, k) = (8, -50).
Therefore, the correct answer is (8, -50).