The problem gives a quadratic equation in factored form: $y = 2.1(x-1)(x-9)$. We need to find the x-intercepts of the graph of this equation and enter them as ordered pairs (points).

AlgebraQuadratic EquationsX-interceptsFactored FormCoordinate Geometry
2025/7/3

1. Problem Description

The problem gives a quadratic equation in factored form: y=2.1(x1)(x9)y = 2.1(x-1)(x-9). We need to find the x-intercepts of the graph of this equation and enter them as ordered pairs (points).

2. Solution Steps

To find the x-intercepts, we need to find the values of xx when y=0y = 0. The equation is given as y=2.1(x1)(x9)y = 2.1(x-1)(x-9). Setting y=0y=0, we get:
0=2.1(x1)(x9)0 = 2.1(x-1)(x-9)
Since 2.12.1 is a constant and not zero, we have:
(x1)(x9)=0(x-1)(x-9) = 0
This equation is satisfied if either (x1)=0(x-1) = 0 or (x9)=0(x-9) = 0.
If (x1)=0(x-1) = 0, then x=1x = 1. The x-intercept is (1,0)(1,0).
If (x9)=0(x-9) = 0, then x=9x = 9. The x-intercept is (9,0)(9,0).
The leftmost x-intercept is the one with the smaller x-value, which is (1,0)(1, 0). The rightmost x-intercept is (9,0)(9, 0).

3. Final Answer

The leftmost x-intercept is (1,0)(1, 0).
The rightmost x-intercept is (9,0)(9, 0).

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