SOLUTION: For the following problem, find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. Write the function in standard form.
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Question 1176688: For the following problem, find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. Write the function in standard form.
Vertex (1,3); passing through (2,6)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Recall that
represents the generalized vertex form.
a = leading coefficient
h = x coordinate of vertex
k = y coordinate of vertex
Since the vertex given to us is (1,3), this means (h,k) = (1,3)
In other words,
h = 1
k = 3
We're also told the parabola passes through (x,y) = (2,6)
x = 2
y = 6
We have these four items of info
h = 1
k = 3
x = 2
y = 6
Plug those four items into the first equation mentioned and isolate 'a'.
The leading coefficient is positive, so the parabola opens upward.
We have
turn into
after plugging in a = 3, h = 1, k = 3
We could expand things out and combine like terms like so
FOIL rule
Distribute
Combine like terms
The vertex form expands and simplifies to the standard form
Graph:
note the vertex is the lowest point at (1,3)
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