Question

For the given graph of $y=a{x}^2+bx+c$ as shown above, $y=$

• A. $x^2+x-2$
• B. $2x^2+4x-2$
• C. $x^2+x-2$

Answer 1

The correct option is C $x^2+x-2$

Given the graph of $y=a{x}^2+bx+c$ as shown below:

Now, the graph of $y$ is an upward opening parabola cutting the $x-$ axis at points $x=-2;x=1$

$\Rightarrow x=-2\&x=1$ are the two roots of the equation
$\therefore$ We can write the equation as $y=a(x-1)(x-(-2\left)\right)\Rightarrow y=a(x-1)(x+2)\cdots \left(1\right)$
Also, the graph passes through $(0,-2)$
$\Rightarrow -2=a(0-1)(0+2)\Rightarrow a=1$
Hence, the equation is given as:
$y=1(x-1)(x+2)=x^2+x-2$