f(x) = -2x^2+4x+1
Can someone explain how the f(x) is worked into this function?
I am supposed to graph the function and find the vertex and the axis of symmetry.I'm a little lost no major.
Take a look here. It's almost the same.
http://www.jiskha.com/display.cgi?id=1489212302
F(x) = Y = -2x^2 + 4x + 1.
a. h = Xv = -B/2A = -4/-4 = 1 = Axis of symmetry.
b. k = -2*1^2 + 4*1 + 1 = 3.
V(h,k) = (1,3).
c. Use the given Eq(Y = -2x^2+4x+1) to calculate "Y" for each value of "X" shown below.
(X,Y).
(-2,
(-1,
(0,1).
(1,3)V.
(2,
(3,
(4,
Use the above points for graphing.
Sure! I can help you understand how the function f(x) is worked into this equation.
In this equation, f(x) represents the output or the function value when you plug in a specific value for x. In other words, f(x) is the y-coordinate of the graph for a given x-coordinate.
Now, let's break down the given function:
f(x) = -2x^2 + 4x + 1
This function is in the form of a quadratic equation, where the highest power of x is 2 (x^2). The main part of the equation is -2x^2, which represents the quadratic term.
The coefficient of x^2 is -2, which means the quadratic term is negative. This tells us that the graph of this function will be a downward-opening parabola.
The coefficient of x, which is 4, represents the linear term. This term affects the slope of the graph.
Lastly, the constant term is 1, which affects the vertical shift of the graph.
To graph the function and find the vertex and axis of symmetry, you can follow these steps:
1. Start by finding the vertex. The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a and b are the coefficients in the quadratic equation. In this case, a = -2 and b = 4. Plugging these values into the formula gives you x = -4 / (2*(-2)) = -4 / (-4) = 1.
So, the x-coordinate of the vertex is 1. To find the y-coordinate of the vertex, substitute this value back into the function: f(1) = -2(1)^2 + 4(1) + 1 = -2 + 4 + 1 = 3.
Therefore, the vertex is (1, 3).
2. The axis of symmetry is a vertical line that passes through the vertex. In this case, the equation of the axis of symmetry is x = 1.
Now that you have the vertex and the axis of symmetry, you can graph the function by plotting several points or using additional properties of quadratic functions.
I hope this explanation helps you in graphing the function and finding the vertex and axis of symmetry! Let me know if you have any further questions.