plot five points
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 plot the points, we first need to find the roots and the vertex of the equation y = x^2 - 8x + 15.
To find the roots, we set y = 0 and solve for x:
0 = x^2 - 8x + 15
0 = (x - 3)(x - 5)
Therefore, the roots are x = 3 and x = 5.
To find the vertex, we use the formula x = -b/2a. In this case, a = 1 and b = -8:
x = -(-8)/(2*1) = 4
Plugging x = 4 back into the equation, we get:
y = 4^2 - 8(4) + 15 = 16 - 32 + 15 = -1
Therefore, the vertex is at (4, -1).
Now we can plot the five points: (3, 0), (5, 0), (4, -1), (0, 15), and (10, 15).
The graph will show an upward opening parabola passing through the roots at (3, 0) and (5, 0), with the vertex at (4, -1). The line y = 15x - 8x + 15 will also be plotted.