Question

Consider the graph. (see photo or formatted text ver below)

For the quadratic equation −2x²−3x+2=0 , complete the table by testing each of the given values to determine whether it is a solution. Identify which one of the values is in the solution set.​

x:
-3/4 | Substituted: ? | Evaluate: ? | True/False: ?

-1/2 | Substituted: ? | Evaluate: ? | True/False: ?

1/2 | Substituted: ? | Evaluate: ? | True/False: ?

Answer 1

`-2x^2-3x+2~~ = ~~0 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x=-\cfrac{3}{4}\hspace{5em}-2\left( -\cfrac{3}{4} \right)^2-3\left( -\cfrac{3}{4} \right)+2~~ = ~~0\implies \cfrac{25}{8}\\e 0 \\\\[-0.35em] ~\dotfill`

`x=-\cfrac{1}{2}\hspace{5em}-2\left( -\cfrac{1}{2} \right)^2-3\left( -\cfrac{1}{2} \right)+2~~ = ~~0\implies 3\\e 0 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{is the only one in the solution set}~\hfill~ }{x=\cfrac{1}{2}\hspace{5em}-2\left( \cfrac{1}{2} \right)^2-3\left( \cfrac{1}{2} \right)+2~~ = ~~0}\implies\qquad 0=0\textit{\LARGE \checkmark}`