If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
a) the discriminant is negative.
b) the discriminant is –3.
c) the discriminant is 0.
d) the discriminant is positive.

The correct option is i.e., .

Further explanation:

Given that is the only -intercept of the graph of a quadratic equation.

The -intercepts is the location where the output of the function is zero that is .

The number of -intercept depends upon the location of the graph.

The discriminant of the quadratic equation is calculated as follows:

If then there are two real roots, if then there are only one real root and if then there will be no real root.

If the discriminant is less than , then the parabola of the quadratic function does not intersect the -axis.

If the discriminant is equal to zero then the parabola will touch the -axis at only one point.

If the discriminant is greater than zero then the parabola will intersect the -axis at two points.

Since, is equal to is the only intercept therefore, the equation is,

In the above equation .

The discriminant of equation (1) is calculated as follows:

Therefore, the discriminant is equal to .

Thus, the correct option is .

Learn more:

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2. A problem to find radius and center of circle  

3. A problem to determine intercepts of a line  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Quadratic equation

Keywords: x-intercept, quadratic function, quadratic equation x= - 3, parabola, discriminant, D>0, D<0, D=0, roots, real roots, equal roots, imaginary roots, curve.

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