Question

What is the coefficient of the shared expression in the parabola's equation whose vertex is at (2, -4) and passes through the point (-3, -1)?

Answer 1

The coefficient of the shared expression in the parabola's equation is 3.59.

Step-by-step explanation:

The equation of the parabola can be written in the form y = ax² + bx + c. We need to find the coefficient of the shared expression, which is the coefficient of x².

To find the coefficient, we can use the vertex form of a parabola equation: y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (2, -4), so the equation becomes y = a(x - 2)² - 4.

Now we can substitute the coordinates of the other point (-3, -1) into the equation and solve for a. -1 = a(-3 - 2)² - 4. Simplifying, we get -1 = 25a - 4. Solving for a, we find a = 3.59.