Question

What is the equation of a parabola that passes through the points (−5, −10), (−3, 2), and (2, −3)? A. y = −x² − 2x + 5 B. y = −x² + 6x − 7 C. y = −189x² − 289x + 353 D. y = −x² − 3x + 2

Answer 1

To find the equation of a parabola that passes through the given points, we can use the general form of a quadratic equation, which is y = ax² + bx + c.

Let's substitute the coordinates of each point into the equation and solve for a, b, and c.

For point (-5, -10):

-10 = a(-5)² + b(-5) + c

For point (-3, 2):

2 = a(-3)² + b(-3) + c

For point (2, -3):

-3 = a(2)² + b(2) + c

Solve this system of equations to find the values of a, b, and c. Once you have those values, you can write the equation of the parabola.

I hope this helps! Let me know if you have any more questions.

Explanation:

let's break it down step by step:

1. For the point (-5, -10):

- Substitute the coordinates into the equation: -10 = a(-5)² + b(-5) + c

2. For the point (-3, 2):

- Substitute the coordinates into the equation: 2 = a(-3)² + b(-3) + c

3. For the point (2, -3):

- Substitute the coordinates into the equation: -3 = a(2)² + b(2) + c

4. Solve the system of equations to find the values of a, b, and c.

5. Once you have the values of a, b, and c, you can write the equation of the parabola in the form y = ax² + bx + c.

I hope this clarifies the step-by-step process! Let me know if you have any other questions.