Find the standard form of the equation of a parabola of the form

y=a(x-h)^2+k
whose vertex is (2,1) and passes through the point (3,2)

Question

Find the standard form of the equation of a parabola of the form

y=a(x-h)^2+k 
whose vertex is (2,1) and passes through the point (3,2)

yttrium · Answer

What do you understand about standard form @Tiara89 ?

anonymous · Answer

absolutely nothin its an online math class and i regret it! @Yttrium

yttrium · Answer

Well. It's just a form of equation that is already expanded and equated to 0.

yttrium · Answer

Let's solve first for a. Since we have given the vertex in form  (h,k) --> (h=2,k=1) and one point at (x=3,y=2) Hence we can solve for a.

yttrium · Answer

@Tiara89 , can you find a?

hero · Answer

Input the vertex and the point in to the equation and solve for a:

2=a(3-2)^2+1
2 = a + 1
a = 1

Now you can write the equation in vertex form:

y = (x - 2)^2 + 1

To write in standard form, simply expand the right side:

y = (x - 2)(x - 2) + 1
y = x(x - 2) - 2(x - 2) + 1
y = x^2 - 2x - 2x + 4 + 1
y = x^2 - 4x + 5

Remember, the standard form of a quadratic equation is
y = ax^2 + bx + c