Graph the equation y, equals, x, squared, minus, 8, x, plus, 15y=x
2
−8x+15 on the accompanying set of axes. You must plot 5 points including the roots and the vertex
To graph the equation y = x^2 - 8x + 15, we first need to find the roots and the vertex.
Step 1: Find the roots
To find the roots, we set y = 0 and solve for x:
0 = x^2 - 8x + 15
0 = (x - 3)(x - 5)
The roots are x = 3 and x = 5.
Step 2: Find the vertex
To find the vertex, we use the formula x = -b/(2a) where a = 1 and b = -8 in this case.
x = -(-8)/(2*1) = 4
Substitute x = 4 back into the equation to find y:
y = 4^2 - 8*4 + 15 = 16 - 32 + 15 = -1
So the vertex is at (4, -1).
Now we can plot the points:
1) (3, 0)
2) (5, 0)
3) (4, -1)
Now we can draw a smooth curve passing through these points to get the graph of the equation y = x^2 - 8x + 15.
The graph will be a parabola opening upwards with roots at x = 3 and x = 5, and the vertex at (4, -1).