Answer:
The correct answer is C. (4, -15)
Step-by-step explanation:
In order to find any vertex, start by finding the x value. We can do this by using -b/2a in which a is the coefficient of x^2 and b is the coefficient of x.
-b/2a
-(-8)/2(1)
8/2
4
Now we know the value of x is 4. This gives us the only option being C
Option C: (4, -15).
Given the quadratic function, y = x² - 8x + 1, where a = 1, b = -8, and c = 1:
Solve for the x-coordinate of the vertex:
We can use the following equation to solve for the x-coordinate of the vertex:
x = -b/2a
Substitute the given values into the formula:
x = -b/2a = -(-8)/2(1) = 8/2 = 4
Hence, the x-coordinate of the vertex is 4.
Solve for the y-coordinate of the vertex:
Next, substitute the x-coordinate of the vertex into the given quadratic function to solve for its corresponding y-coordinate:
y = x² - 8x + 1
y = (4)² - 8(4) + 1
y = 16 - 32 + 1
y = -15
Therefore, the vertex of the given quadratic function, y = x² - 8x + 1, is: x = 4, y = -15, or (4, -15).
We find the vertex of a quadratic equation with the following steps:
1. Get the equation in the form y = ax2 + bx + c.
2. Calculate -b / 2a. This is the x-coordinate of the vertex.
3. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
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