Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

Question

Write the standard form of the equation of the parabola that has a vertex at  and passes through the point  .

Quizplus · Accepted Answer

The standard form of a parabola is written as y = a(x-h)^2+k, where (h,k) is the vertex.

From the given information, we know that the vertex is (11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11) and that the parabola passes through the point (11ec1854_fdcf_b551_acfc_fff78c6705ba_TBX8702_11).

Using the vertex form, we can find a by substituting the x and y values of the point that the parabola passes through:

11ec1854_fdcf_b551_acfc_fff78c6705ba_TBX8702_11 = a(11ec1854_fdcf_b551_acfc_fff78c6705ba_TBX8702_11 - 11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11)^2 + 11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11

11ec1854_fdcf_b551_acfc_fff78c6705ba_TBX8702_11 = a(1)^2 + 11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11

11ec1854_fdcf_b551_acfc_fff78c6705ba_TBX8702_11 - 11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11 = a

a = 11ec1854_fdcf_db64_acfc_2f3aecaec814_TBX8702_11

Therefore, the equation of the parabola in standard form is y = 11ec1854_fdcf_db64_acfc_2f3aecaec814_TBX8702_11(x-11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11)^2 + 11ec1854_fdcf_b550_acfc_9f5cdd315c6c_TBX8702_11.

Write the Standard Form of the Equation of the Parabola