Question

Find the equation of the parabola that goes through the given points (1, 2), (0, 5), and (1, 14).

a) y = 5x² - 3x + 4
b) y = -x² + 7x + 5
c) y = 2x² + 5
d) y = 3x² - x + 2

Answer 1

To find the equation of the parabola that goes through the given points, substitute the values of the points into the general form of a quadratic equation and solve the system of equations.

Step-by-step explanation:

To find the equation of the parabola that goes through the given points (1, 2), (0, 5), and (1, 14), we can use the general form of a quadratic equation, y = ax^2 + bx + c, and substitute the values of the points into the equation to form a system of equations.

Using the points (1, 2), (0, 5), and (1, 14), we can form the following equations:

• a + b + c = 2
• b + c = 5
• a + b + c = 14

Solving this system of equations, we find that a = -1, b = 7, and c = 4.

Therefore, the equation of the parabola is y = -x^2 + 7x + 4.