Question

Write the equation of the parabola that satisfies the given criteria: x-intercepts (2,0) and (-4,0) passes through: (-1,-3)

Answer 1

To find the equation of a parabola given the x-intercepts and a point on the parabola, use the standard form of a quadratic equation and substitute the given values into the equation to form a system of equations. Solve the system of equations to find the values of a, b, and c, and then substitute them back into the equation to obtain the equation of the parabola.

Step-by-step explanation:

The student is given the x-intercepts (2,0) and (-4,0) and a point on the parabola (-1,-3). To find the equation of the parabola, we can use the standard form of a quadratic equation: y = ax^2 + bx + c. We substitute the given points into the equation to form a system of equations, and then solve for a, b, and c.

1. Using the point (-1,-3), we substitute the values into the equation to form the equation -3 = a(-1)^2 + b(-1) + c.
2. Using the x-intercept (2,0), we substitute the values into the equation to form the equation 0 = a(2)^2 + b(2) + c.
3. Using the x-intercept (-4,0), we substitute the values into the equation to form the equation 0 = a(-4)^2 + b(-4) + c.
4. We now have a system of three equations with three variables. Solve the system of equations to find the values of a, b, and c.

Once you have the values of a, b, and c, substitute them back into the equation y = ax^2 + bx + c to obtain the equation of the parabola.