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)= (x-3)2 -3
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)= (x-3)2 -3
Here, h = 3, k = -3 and a = 1
So, the vertex of the parabola is (3,-3) and the axis of the symmetry is x = 3. As a > 0 so the graph is open upwards.
As a =1, the width of the function F(x)= 2(x+1)2 +4 is same as the width of the parent function f(x) = x2.
Final Answer:
Hence, the vertex of the parabola is (3,-3), the axis of the symmetry is x = 3, the graph is open upwards and the width of the function G(x)= (x-3)2-3 is same as the width of the parent function f(x) = x2.
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The values for various parameters are calculated using quadratic functions. They are depicted graphically by a parabola. The coefficient determines the direction of the curve with the highest degree. From the word "quad," which means square, comes the word "quadratic." In other words, a "polynomial function of degree 2" is a quadratic function. Quadratic functions are used in numerous contexts.
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