Answer:
The point of interception of the graph and x axis are -2.366 and -0.634.
The only graph that satisfy this conditions is Graph A
Step-by-step explanation:
Given the equation;
[tex]y = 2x^2 + 6x + 3\\[/tex]
at y = 0
[tex]2x^2 + 6x + 3=0\\[/tex]
the roots of the quadratic equation (at y =0) can be calculated using the quadratic formula;
[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Using the quadratic equation to solve for the roots;
[tex]x = \frac{-6\pm \sqrt{6^2 -4*2*3}}{2*2}\\x = \frac{-6\pm \sqrt{36 - 24}}{4}\\x = \frac{-6\pm \sqrt{12}}{4}\\so, we have \\x = -2.366\\or\\x = -0.634\\[/tex]
Therefore, the point of interception of the graph and x axis are -2.366 and -0.634.
The only graph that satisfy this conditions is Graph A
