Maths-
General
Easy
Question
How can you determine the values of h and k from the graph shown? Write the function for the parabola.
Hint:
The vertex form of a quadratic function is
f(x) = a(x – h)2 + k
Where a, h, and k are constants. Here, h represents horizontal translation, a represents vertical translation and (h,k) is the vertex of the parabola. Also, a represents the Vertical stretch/shrink of the parabola and if a is negative, then the graph is reflected over the x-axis.
The correct answer is: Hence, the function of the parabola is f(x) = (x-3)2 - 2
h and k are the vertex of the parabola. So, by seeing the graph we can conclude that the vertex is (3,-2).
So, h = 3 and k = -2
Let’s say that function of the parabola is f(x) = a(x-3)2 - 2
By seeing the graph, we can conclude that point (1,2) lies on the parabola and this can be used to find the value of a
2 = a(1-3)2 - 2
4a = 4
a = 1
Final Answer:
Hence, the function of the parabola is f(x) = (x-3)2 - 2
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