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

Since the vertex is given, the equation can be written in the form: 
y = a(x - h)^2 + k, where (h,k) is the vertex 
Plugging in the given vertex: 
y = a(x - 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11)^2 + 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 
Next, substitute the point that the parabola passes through: 
11eb80b1_b056_8943_a291_5759f13c32bd_TB8633_11 = a(11eb80b1_b056_8943_a291_5759f13c32bd_TB8633_11 - 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11)^2 + 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 
Simplifying: 
11eb80b1_b056_8943_a291_5759f13c32bd_TB8633_11 = a(1)^2 + 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 
11eb80b1_b056_8943_a291_5759f13c32bd_TB8633_11 = a + 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 
Subtracting 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 from both sides: 
11eb80b1_b056_d768_a291_850e25ce07bf_TB8633_11 = a 
Thus, the equation is: 
y = 11eb80b1_b056_d768_a291_850e25ce07bf_TB8633_11(x - 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11)^2 + 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 
which can be rewritten in standard form: 
y - 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11 = 11eb80b1_b056_d768_a291_850e25ce07bf_TB8633_11(x - 11eb80b1_b056_8942_a291_15823d0efd2e_TB8633_11)^2

Write the Standard Form of the Equation of the Parabola