Question

question 19 of 25
the graph of a certain quadratic function has no x-intercepts. which of the following are possible values for the discriminant? check all that apply.

a. -7

b. 18

c. -25

d. 0

Explanation:

Step1: Recall discriminant rules

For a quadratic function \(y = ax^2 + bx + c\), the discriminant is \(D = b^2 - 4ac\). The number of \(x\)-intercepts is determined by:

• If \(D>0\), two distinct \(x\)-intercepts.
• If \(D = 0\), one \(x\)-intercept.
• If \(D<0\), no \(x\)-intercepts.

Step2: Analyze each option

• Option A: \(-7<0\), so discriminant \(-7\) means no \(x\)-intercepts.
• Option B: \(18>0\), so two \(x\)-intercepts.
• Option C: \(-25<0\), so discriminant \(-25\) means no \(x\)-intercepts.
• Option D: \(0\) means one \(x\)-intercept.

Answer:

A. -7, C. -25