Question
Sketch the graph of each function :
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 graph of h(x) is plotted above
F(x)= 2(x-1)2 +4
Given, F(x)= 2(x-1)2 +4
Here, h = 1, k = 4 and a = 2
So, the vertex of the parabola is (1,4) and the axis of the symmetry is x = 1. As a > 0, so h(x) with open upwards.
The graph can be plotted as
Final Answer:
Hence, the graph of h(x) is plotted above.
Related Questions to study
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¶The parent quadratic function connects the points whose coordinates have the form f(x) = x2 and is of the form (number, number2). This function, which typically takes f(x) = a(x - h)2 + k, can be transformed. It can also be changed to f(x) = ax2 + bx + c. In the following sections, let's examine each of these in greater detail.
A computer game designer uses the function f(x)= 4(x-2)2+6 to model the path of the fish. At what other point does the squid’s path intersect the path of the fish?
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.
¶The parent quadratic function connects the points whose coordinates have the form f(x) = x2 and is of the form (number, number2). This function, which typically takes f(x) = a(x - h)2 + k, can be transformed. It can also be changed to f(x) = ax2 + bx + c. In the following sections, let's examine each of these in greater detail.
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The locations whose coordinates are of the form are connected by the parent quadratic function, which has the form f(x) = x2 (number, number2). The parent quadratic function joins the places whose coordinates have the form f(x) = x2 (number, number2). This function, which generally has the form f(x) = a (x - h)2 + k, can be transformed to take the form f(x) = ax2 + bx + c.
Suppose a goalie kicks a soccer ball. The ball travels in a parabolic path from point (0,0) to (57,0). Consider a quadratic function in vertex form for the path of the ball. Which values can you determine? What values are you unable to determine? Explain.
A polynomial function is referred to as quadratic if it has one or more variables and a variable with a maximum exponent of two. It is sometimes referred to as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
The locations whose coordinates are of the form are connected by the parent quadratic function, which has the form f(x) = x2 (number, number2). The parent quadratic function joins the places whose coordinates have the form f(x) = x2 (number, number2). This function, which generally has the form f(x) = a (x - h)2 + k, can be transformed to take the form f(x) = ax2 + bx + c.
