Question
Identify the vertex, axis of symmetry and direction of the graph of each function, Compare the width of the graph to the width of the graph of f(x)= x2
G(x)= -0.75(x-5)2 +6
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 axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
The correct answer is: f(x) = x2
Parent function is f(x) = x2
Given, G(x)= -0.75(x-5)2 +6
Here, h = 5, k = 6 and a = -0.75
So, the vertex of the parabola is (5,6) and the axis of the symmetry is x = 5. As a < 0 so the graph is open downwards.
As a < 1, the width of the function G(x)= -0.75(x-5)2+6 is more then the width of the parent function f(x) = x2.
Final Answer:
Hence, the vertex of the parabola is (5,6), the axis of the symmetry is x = 5, the graph is open downwards and the width of the function G(x)= -0.75(x-5)2+6 is more then the width of the parent function f(x) = x2.
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