Answer: Write a quadratic function in vertex form whose graph has the vertex (1,2) and passes through the point (3,10). (what does F(x)=?) Algebra -> Quadratic Equations and Parabolas -> SOLUTION: Write a quadratic function in vertex form whose graph has the vertex (1,2) and passes through the point (3,10).
Step-by-step explanation:
By using the given information, we will see that the quadratic equation is:
y = 5*(x - 3)^2 + 2
We know that for a parabola with a vertex (h, k), the equation in the vertex form can be written as:
y = a*(x - h)^2 + k
In this case, the vertex is (3, 2), so we have:
Replacing that in the general equation we get:
y = a*(x - 3)^2 + 2
Now, we also know that the equation must pass through the point (4, 7), then we have that:
7 = a*(4 - 3)^2 + 2
Now we can solve that to get the value of a:
7 = a*1^2 + 2
7 = a + 2
7 - 2 = a = 5
So the quadratic equation is:
y = 5*(x - 3)^2 + 2
If you want to learn more about quadratic equations, you can read:
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