How do you write the quadratic equation given Vertex: (-2,0) Passing through: (0,3)?

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Answer 1 · 2016-03-18T10:21:18

The required quadratic equation
#y=3/4x^2+3x+3#

From the given vertex #(h, k)=(-2, 0)# and passing thru #(0, 3)#

A little inspection tells us that the vertex is lower than the given point. We can conclude that the parabola opens upward.

#(x-h)^2=+4p(y-k)#

Let us use the two given points to solve for p:

#(x-h)^2=+4p(y-k)#
#(0--2)^2=+4p(3-0)#
#4=4p*3#

#4=12p#
#p=1/3#

Now we can write the equation
#(x-h)^2=+4p(y-k)#
#(x--2)^2=4(1/3)(y-0)#
#y=3/4(x^2+4x+4)#

#y=3/4x^2+3x+3#

God bless....I hope the explanation is useful.