Question

Find an equation for the parabola that passes through the point (-3.4)

Answer 1

To find an equation for the parabola that passes through the point (-3, 4), we can use the vertex form of a parabola equation and substitute the given values to solve for the constant term a.

Step-by-step explanation:

To find an equation for the parabola that passes through the point (-3, 4), we need to use the vertex form of a parabola equation, which is y =
`a(x-h)^2 + k.`, the vertex (h, k) is the point (-3, 4). Substituting these values into the equation, we get y =
`a(x+3)^2 + 4.`

Next, we can use another point on the parabola to solve for the value of a. Let's use the point (0, 1). Substituting these values into the equation, we get 1 =
`a(0+3)^2 + 4,`es to 1 = 9a + 4.

Solving for a, we subtract 4 from both sides to get 9a = -3. Dividing by 9, we find that a = -1/3. Therefore, the equation of the parabola that passes through the point (-3, 4) is y =
`(-1/3)(x+3)^2 + 4.`