To graph the quadratic equation [tex]\(y = 3x^2 - 5x - 3\)[/tex] and find its [tex]\(x\)[/tex]-intercepts, follow these steps:
1. Open the Graphing App:
Begin by opening your preferred graphing app or tool.
2. Input the Equation:
Type the equation into the graphing app exactly as:
[tex]\[
y = 3x^{\wedge}2 - 5x - 3
\][/tex]
Make sure to use the [tex]\(\wedge\)[/tex] key for exponents and to press Enter to update the graph.
3. Zoom In on the Graph:
Use the zoom function in your graphing app (for example, two-finger swipe up or down on a Chromebook) to zoom in very close to the points where the graph crosses the [tex]\(x\)[/tex]-axis. These points are your [tex]\(x\)[/tex]-intercepts.
4. Estimate the [tex]\(x\)[/tex]-Intercepts:
Carefully estimate the points where the graph intersects the [tex]\(x\)[/tex]-axis. These points should be in the format [tex]\((x, 0)\)[/tex].
Based on the graph and a detailed inspection, the estimated [tex]\(x\)[/tex]-intercepts for the equation [tex]\(y = 3x^2 - 5x - 3\)[/tex] are approximately at:
[tex]\[
(2.1, 0) \quad \text{and} \quad (-0.5, 0)
\][/tex]
So, the estimated [tex]\(x\)[/tex]-intercepts are at:
[tex]\[
\boxed{2.1}, \; \text{and} \boxed{-0.5}
\][/tex]
