Find the quadratic function that has the vertex (4,5) and passes through the point (8,21) If possible, can you explain the work?
Thanks! *71 POINTS!*
1 answer:
Start by looking at the vertex form of a quadratic function, f(x) = a(x - h)^2 + k. The variables h and k are the values of the vertex. Plug those in to get f(x) = a(x - 4)^2 + 5. To find the variable a, plug in the point given for the x and y values. So, you get (21) = a((8) - 4)^2 + 5. Solve for a algebraically, and you get a = 1. Finally, plug everything in and simplify the equation. You should get that the quadratic function is f(x) = x^2 - 8x + 21. Hope this helps!
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Answer:
k = 8
Step-by-step explanation:
For the points to be collinear, then the slopes of each pair of points must be equal.
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (2, 6)
m = =
= 1
Repeat with
(x₁, y₁ ) = (2, 6) and (x₂, y₂ ) = (4, k)
m = =
, thus
= 1 ( multiply both sides by 2 )
k - 6 = 2 ( add 6 to both sides )
k = 8