Question

Sketch the graph of 2 x squared minus 3 x minus 9 using your graphing calculator. What are the x-intercepts of this graph?

a.
Negative 3, negative three-halves
b.
Negative 3, three-halves
c.
3, Three-halves
d.
3, Negative three-halves

Answer 1

The graph of the equation y = 2x² - 3x - 9 is attached

The roots are A (-1.5, 0) and B(3, 0)

What are roos of parabolic equations

The roots of quadratic equation are the values of x that results to y =0

In a graph, these are points that are called x-intercepts. In other words, this is where the parabolic equation intersects or cuts the x-axis.

In the graph, the points are labeled A and B. The coordinates of these points are

A (-1.5, 0) and B(3, 0)

Answer 2

`\textsf{d)} \quad 3, -(3)/(2)`

Explanation:

To sketch the graph of y = 2x² - 3x - 9 using a graphing calculator, enter the equation into the calculator and graph it by selecting the appropriate function or plotting options. (See attachment).

The x-intercepts of a graph are x-values at which the graph intersects the x-axis. From inspection of the plotted graph, the x-intercepts are:

`\Large\boxed{\boxed{x=3,\;\; x=-(3)/(2)}}`

`\hrulefill`

As the x-intercepts are the points on the graph where y = 0, to find the x-intercepts algebraically, set the quadratic function to zero, then solve for x:

`\begin{aligned}2x^2-3x-9&=0\\2x^2+3x-6x-9&=0\\x(2x+3)-3(2x+3)&=0\\(x-3)(2x+3)&=0\\\\x-3&=0 \implies x=3\\2x+3&=0 \implies x=-(3)/(2)\end{aligned}`

This confirms that the x-intercepts are 3 and -³/₂.