What are the key points on the graph of y = x^2 – 8x? Name the vertex, x-intercepts, and y-intercept.
• X-intercepts: (0,0) (8,0)
Vertex: (4,-16)
There is no y-intercept.
• X-intercepts: (0,0) (8,0)
y-intercept: (0,0)
vertex: (4,-16)
• X-intercept: (4,-16)
y-intercept: (0,0)
vertex: (8,0)
• X-intercept: (0,8)
y-intercept: (0,0)
vertex: (4,-16)
The correct answer is:
• X-intercepts: (0,0) (8,0)
Vertex: (4,-16)
There is no y-intercept.
The correct answer is:
X-intercepts: (0,0) and (8,0)
Y-intercept: There is no y-intercept.
Vertex: (4,-16)
To find the key points on the graph of y = x^2 - 8x, we need to consider the x-intercepts, the y-intercept, and the vertex.
The x-intercepts are the points where the graph intersects the x-axis. To find the x-intercepts, we set y = 0 and solve the equation:
0 = x^2 - 8x
Factoring the equation, we get:
0 = x(x - 8)
So, the x-intercepts are (0, 0) and (8, 0).
The y-intercept is the point where the graph intersects the y-axis. To find the y-intercept, we set x = 0 and solve the equation:
y = 0^2 - 8(0)
Simplifying, we find that the y-intercept is (0, 0).
The vertex is the highest or lowest point on the parabola. To find the vertex, we can use the formula: x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -8.
x = -(-8) / (2*1) = 8 / 2 = 4
To find the y-coordinate of the vertex, we substitute x = 4 into the equation:
y = (4)^2 - 8(4)
y = 16 - 32 = -16
Therefore, the vertex is (4, -16).
Combining all this information, the correct answer is:
X-intercepts: (0,0), (8,0)
Vertex: (4,-16)
Y-intercept: (0,0)