Question

Each of the following quadratic equations represents the graph shown. Which equation reveals the exact values of the $x-$intercepts of the graph?

• A. $y=\frac{1}{2}(2x-5)(x+1)$
• B. $y=2x^2-\frac{3}{2}x-5$
• C. $y={(x-\frac{3}{4})}^2$
• D. $y={(x-\frac{3}{2})}^2-\frac{9}{16}$

Answer 1

The correct option is A $y=\frac{1}{2}(2x-5)(x+1)$

From the graph the roots are $x=-1,\frac{5}{2}$, Now at $x=0$ we have $y=\frac{-5}{2}$

$\Rightarrow y=a(x-\frac{5}{2})(x+1)$

$x=0\Rightarrow y=\frac{-5}{2}=a\frac{-5}{2}\left(1\right)\Rightarrow a=1$

$\therefore y=(x-\frac{5}{2})(x+1)=\frac{(2x-5)(x+1)}{2}$