What are the steps to graphing this quadratic equation? Y=(-2x)^2
It is a parabola U. See what happens with the y's when you use 0, +1, and -1 for the x's.
Y = (-2X)^2 = 4X^2.
1. Calculate coordinates of the vertex:
h = Xv = -b / 2a = o/8 = 0.
K = Yv = 4(0)^2 = 0. So the vertex is
at the origin. V(h.k) = (0 , 0).
2. Select values of X on both sides
of vertex and cal. the corresponding
value of Y using the given Eq.
(-2 , 16) , (-1 , 4) , (0 , 0) ,
(1 , 4) , (2 , 16).
The graph should show a Y-parabola
that opens upward with vertex at the
origin.
To graph the quadratic equation y = (-2x)^2, you can follow these steps:
Step 1: Understand the equation
The given equation is in the standard form y = ax^2, where a is the coefficient of the quadratic term. In this case, a = (-2)^2 = 4.
Step 2: Find the vertex
The vertex of a quadratic equation in the form y = ax^2 is given by the coordinates (h, k), where h = -b/2a and k is the value of y when x = h.
In this case, the coefficient of x is 0 since (-2x)^2 can be simplified as (2x)^2 which equals 4x^2. So, the equation doesn't have a linear term or a constant term. Therefore, the vertex of this equation can be found at the origin (0, 0).
Step 3: Determine the direction of the parabola
Since the coefficient of the quadratic term (a) is positive (4), the parabola opens upwards.
Step 4: Plot points on the graph
To plot some points on the graph, substitute different x-values into the equation and calculate the corresponding y-values. For example:
- When x = -2, y = (-2(-2))^2 = 4^2 = 16. This gives us the point (-2, 16).
- When x = -1, y = (-2(-1))^2 = 2^2 = 4. This gives us the point (-1, 4).
- When x = 0, y = (-2(0))^2 = 0^2 = 0. This gives us the vertex (0, 0).
- When x = 1, y = (-2(1))^2 = -2^2 = 4. This gives us the point (1, 4).
- When x = 2, y = (-2(2))^2 = -4^2 = 16. This gives us the point (2, 16).
Step 5: Plot the points and draw the graph
On a coordinate plane, plot the calculated points (-2, 16), (-1, 4), (0, 0), (1, 4), and (2, 16). Then, connect the points smoothly to form a parabolic curve that opens upwards.
Note: You can also plot additional points if desired for a more accurate and refined graph.
That's it! You have graphed the quadratic equation y = (-2x)^2.