Question

if x=-3 is the only x-incercept of the graph of a quadratic equation which statement best describes the discrinant of the equation

Answer 1

Answer:

The discriminant must be zero.

Step-by-step explanation:

Quadratic Equation

The standard representation of a quadratic function is:

$f(x)=ax^2+bx+c$

where a,b, and c are constants.

The zeros, roots, or x-intercepts can be found by solving the equation:

$ax^2+bx+c=0$

We can use the quadratic formula to find the roots:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Note this formula gives us two different roots if the square root is non-zero.

The only way there can be only one x-intercept is because the square root is zero.

If the square root is zero, then

$b^2-4ac =0$

The expression is called the discriminant.

Thus, if x=-3 is the only x-intercept of the graph of a quadratic function, then the discriminant must be zero.