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The vertex form of the quadratic function f (x) = x² + 8x + 7 is

f(x)= a(x-h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?

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Answer:

Explanation:

The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.

To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:

h = -8 / 2(1) = -4

Therefore, the value of h is -4.

Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:

k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9

Therefore, the value of k is -9.

Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:

f(x) = a(x - h)² + k

x² + 8x + 7 = a(x - (-4))² + (-9)

We can then distribute the squared term and simplify the equation to get:

x² + 8x + 7 = a(x² - 8x + 16) + (-9)

x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)

We can then collect like terms to get:

x² + 8x + 7 = a(x²) - 8ax + 16a - 9

Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.

Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.

User Emilis Vadopalas
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