Question
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?
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 squid’s path intersects the path of the fish at (5, 42) and (-1, 42)
The path of the fish is given as f(x)= 4(x-2)2+6.
It is also given that fish and squid intersect at (5,42). The path of fish intersects at two points and both these points have same y-coordinate
So, 42 = 4(x-2)2+6
4(x-2)2 = 36
(x-2)2 = 9
x-2 = 3
x = 3 + 2 and x = -3 +2
x = 5 and x = -1
Final Answer:
Hence, the squid’s path intersects the path of the fish at (5, 42) and (-1, 42).
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.
Related Questions to study
How does the graph of g(x)= x2 - 4 compare to that of f(x) = x2
How does the graph of g(x)= x2 - 4 compare to that of f(x) = x2
Solve the following simultaneous equations graphically :
2X+Y-3=0
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Solve the following simultaneous equations graphically :
2X+Y-3=0
3X+2Y-4= 0
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.
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.
