Question

If the curve described by the equation $y=x^2+bx+c$ cuts the $x-$ axis at $-4$ and $y-$ axis at $4$, at which other point does it cut the $x-$ axis?

• A. -1
• B. 4
• C. 1
• D. -4

Answer 1

The correct option is A -1

$y=x^2+bx+c$ is a quadratic equation and the equation represents a parabola.
The $x$ coordinate of the point where it cuts the $y$ axis = 0 Therefore, $(0,4)$ is a point on the curve and will satisfy the equation. Substitute $y=4$ and $x=0$ in the quadratic equation, $4=0^2+b\left(0\right)+c$ or $c=4$.
The $y$ coordinate of the point where it cuts the $x$ axis = 0. Therefore $(-4,0)$ lies on the curve, Substituting the values in equation, $0=(-4{)}^2+b(-4)+4$.
Therefore $b=5$ Quadratic equation: $y=x^2+5x+4$.
If we substitute $x=-1$, quadratic equation becomes 0.