Question

Eqution of parabola that passes through (6,27) and a vertex of (2,-5) in quadratic form

Answer 1

To find the equation of a parabola that passes through a given point and has a given vertex in quadratic form, substitute the coordinates into the equation and solve for the constants.

Step-by-step explanation:

The equation of a parabola in quadratic form is given by y = ax^2 + bx + c where a, b, and c are constants. To find the equation of a parabola that passes through (6,27) and has a vertex of (2,-5), we can substitute these values into the equation and solve for a, b, and c.

Step 1: Substitute the coordinates of the vertex into the equation to get -5 = 4a + 2b + c.

Step 2: Substitute the coordinates of (6,27) into the equation to get 27 = 36a + 6b + c.

Step 3: Solve the system of equations formed by the two equations obtained in steps 1 and 2 to find the values of a, b, and c.

Step 4: Substitute the values of a, b, and c into the equation to get the final equation of the parabola in quadratic form.