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

Question

Eli Assouline · Accepted Answer

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.

Genesis Allen · Answer

undefined To write the quadratic equation given the vertex (-2, 0) and passing through (0, 3), you can use the vertex form of a quadratic equation, which is $y = a(x - h)^2 + k$, where (h, k) is the vertex. Substituting the given vertex coordinates into the equation, we get $y = a(x + 2)^2$. Then, use the given point (0, 3) to find the value of 'a'. Substitute the coordinates of the point into the equation and solve for 'a'. We have $3 = a(0 + 2)^2$. Solving this equation gives $a = \frac{3}{4}$. Therefore, the quadratic equation is $y = \frac{3}{4}(x + 2)^2$.