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
H(x)= -3(x+2)2 – 5
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, H(x)= -3(x+2)2 – 5
Here, h = -2, k = -5 and a = -3
So, the vertex of the parabola is (-2,-5) and the axis of the symmetry is x = -2. As a < 0 so the graph is open downwards.
As a > 1, the width of the function H(x)= -3(x+2)2 – 5 is less then the width of the parent function f(x) = x2.
Final Answer:
Hence, the vertex of the parabola is (-2,-5), the axis of the symmetry is x = -2, the graph is open downwards and the width of the function H(x)= -3(x+2)2–5 is less then the width of the parent function f(x) = x2.
Related Questions to study
Solve the following simultaneous equations graphically :
3X+2Y=13
X+2Y=7
Solve the following simultaneous equations graphically :
3X+2Y=13
X+2Y=7
Sketch the graph of each function :
Sketch the graph of each function :
How does the graph of g(x) = x2+3 compare to that of f(x) = x2
How does the graph of g(x) = x2+3 compare to that of f(x) = x2
Sketch the graph of each function :
Sketch the graph of each function :
Sketch the graph of each function f(x)= 0.5(x+2)2+2
Sketch the graph of each function f(x)= 0.5(x+2)2+2
Solve the following simultaneous equations graphically :
X+2Y=5
2X+Y=4
Solve the following simultaneous equations graphically :
X+2Y=5
2X+Y=4
How does the graph of g(x) = x2 - 3 compare to that of f(x) = x2
How does the graph of g(x) = x2 - 3 compare to that of f(x) = x2
Sketch the graph of the function h(x)= -2(x-2)2 -2
Sketch the graph of the function h(x)= -2(x-2)2 -2
Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, then find the distance between their tops.
Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, then find the distance between their tops.
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.
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.
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
3X+2Y-4= 0
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.
