Question

Question for 60 Points

Answer 1

Using the Factor Theorem to find the equation of the parabola, we have that:

$a + b + c = -\frac{48}{7}$

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

In this problem, we have a horizontal parabola, defined as follows:

$f(y) = a(y - y_1)(y - y_2)$.

The roots are $y_1 = -1, y_2 = -7$, hence:

f(y) = a(y + 1)(y + 7)

f(y) = a(y² + 8y + 7).

The x-intercept is of x = -3, hence f(0) = -3, so:

$-3 = 7a$

$a = -\frac{3}{7}$

Then the equation is:

$x = -\frac{3}{7}y^2 - \frac{24}{7}x - 3$

Then the sum of the coefficients is:

$a + b + c = -\frac{3}{7} - \frac{24}{7} - \frac{21}{7} = -\frac{48}{7}$

More can be learned about the Factor Theorem at brainly.com/question/24380382

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