How do i plot this graphic quadratic equation y=x^2-8x+12.I have tried but i end up failing.Please help me and explain in detail plz help out.
there are lots of online graphing sites. Just type your equation in at wolframalpha.com
It will show you all you want to know about that graph.
Though I fail to see how you could have tried and failed. Can you not plot points and connect them, knowing that this is a parabola?
x^2-8x+12 = 0. 12 = -2*(-6). -2 + (-6) = = -8 = B.
(x-2)(x-6) = 0
x-2 = 0, X = 2.
x-6 = 0, X = 6.
roots: (2, 0), (6, 0).
Y-int. = (0,12). (8,12).
h = -B/2A = 8/2 = 4.
k = 4^2-8*4 + 12 = -4.
V(h, k) = V(4, -4).
Graph: (0,12), (2,0), V(4,-4), (6,0), (8,12).
To plot the graph of the quadratic equation y = x^2 - 8x + 12, you will need to follow a step-by-step process. Here's how you can do it:
Step 1: Determine the vertex:
The vertex of a quadratic equation in the form y = ax^2 + bx + c is given by the formula:
Vertex = (-b/2a, f(-b/2a))
In your equation, a = 1, b = -8, and c = 12.
To find the x-coordinate of the vertex, use the formula:
x = -b/2a = -(-8) / (2 * 1) = 8/2 = 4.
Now, substitute this value of x into the equation to find the y-coordinate:
y = (4)^2 - 8(4) + 12 = 16 - 32 + 12 = -4.
So, the vertex is (4, -4).
Step 2: Find the y-intercept:
To find the y-intercept, set x = 0 in the equation:
y = (0)^2 - 8(0) + 12 = 0 - 0 + 12 = 12.
So, the y-intercept is (0, 12).
Step 3: Determine additional points:
You can find a few more points to plot by substituting different x-values into the equation. Let's choose x = 1 and x = 7:
For x = 1:
y = (1)^2 - 8(1) + 12 = 1 - 8 + 12 = 5.
So, the point is (1, 5).
For x = 7:
y = (7)^2 - 8(7) + 12 = 49 - 56 + 12 = 5.
So, the point is (7, 5).
Step 4: Plot the points and draw the graph:
Now that you have the vertex, y-intercept, and a couple more points, you can plot them on a coordinate system. Place the points on the graph and connect them smoothly to create a curve.
Here's a visual representation of the graph:
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1 4 7
I hope this step-by-step explanation helps you plot the quadratic equation successfully.