Question

quadratics: the discriminant notes + practice
the discriminant tells us the number of _______ that a quadratic function has
the root(s) of a function refer to the ______ intercept(s)
the discriminant can be either _____, _____ or zero
to find the discriminant, utilize a portion of the __________ formula
discriminant notes
$d = b^2 - 4ac$
$d > 0$ 2 real roots
$d = 0$ 1 real root
$d < 0$ 2 complex roots
identifying: determine how many roots a function would have with the following discriminant values:

discriminant value	number of roots
$d = 0$
$d = -12$
$d = 1/2$

Explanation:

Step1: Analyze \( D = 5 \)

Check the sign of \( D \). Since \( 5>0 \), from the notes \( D>0 \) means 2 real roots.

Step2: Analyze \( D = 0 \)

Check the sign of \( D \). Since \( D = 0 \), from the notes \( D = 0 \) means 1 real root.

Step3: Analyze \( D=- 12 \)

Check the sign of \( D \). Since \( - 12<0 \), from the notes \( D<0 \) means 2 complex roots.

Step4: Analyze \( D=\frac{1}{2} \)

Check the sign of \( D \). Since \( \frac{1}{2}>0 \), from the notes \( D>0 \) means 2 real roots.

Answer:

Discriminant Value	Number of Roots
\( D = 0 \)	1 real root
\( D=-12 \)	2 complex roots
\( D=\frac{1}{2} \)	2 real roots