Card 1 of 20
EasyStudy card 1
Prompt
State the quadratic formula.
Answer
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\).
MathChapter 11: Quadratic Functions
Flashcards
Quadratic Formula and the Discriminant Flashcards
Twenty cards on formula anatomy, root count, exact roots, and root relationships.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is the discriminant?
Answer
\(D=b^2-4ac\).
Card 3 of 20
EasyStudy card 3
Prompt
What does \(D>0\) mean?
Answer
Two distinct real roots.
Card 4 of 20
EasyStudy card 4
Prompt
What does \(D=0\) mean?
Answer
One repeated real root.
Card 5 of 20
EasyStudy card 5
Prompt
What does \(D<0\) mean?
Answer
No real roots.
Card 6 of 20
EasyStudy card 6
Prompt
How does \(D>0\) appear on a parabola?
Answer
It crosses the horizontal axis twice.
Card 7 of 20
EasyStudy card 7
Prompt
How does \(D=0\) appear on a parabola?
Answer
It touches the horizontal axis once.
Card 8 of 20
MediumStudy card 8
Prompt
What is the sum of roots of \(ax^2+bx+c=0\)?
Answer
\(r_1+r_2=-\frac ba\).
Card 9 of 20
MediumStudy card 9
Prompt
What is the product of roots?
Answer
\(r_1r_2=\frac ca\).
Card 10 of 20
MediumStudy card 10
Prompt
What condition creates exactly one real root?
Answer
Set \(D=0\).
Card 11 of 20
MediumStudy card 11
Prompt
What is the coefficient-sign rule before formula substitution?
Answer
Record \(a,b,c\) with their signs from standard form.
Card 12 of 20
MediumStudy card 12
Prompt
What is the denominator trap?
Answer
The whole numerator is divided by \(2a\).
Card 13 of 20
MediumStudy card 13
Prompt
What is the discriminant sign trap?
Answer
Use \(b^2-4ac\), not \(b^2+4ac\).
Card 14 of 20
MediumStudy card 14
Prompt
When should you avoid solving both roots?
Answer
When the question asks only for root count, sum, or product.
Card 15 of 20
MediumStudy card 15
Prompt
Why keep exact radicals?
Answer
They preserve exact values and often simplify cleanly.
Card 16 of 20
MediumStudy card 16
Prompt
For \(2x^2-7x+3=0\), what is \(b\)?
Answer
\(b=-7\).
Card 17 of 20
HardStudy card 17
Prompt
Find the sum of roots of \(3x^2+12x-5=0\).
Answer
\(-4\).
Card 18 of 20
HardStudy card 18
Prompt
Find the product of roots of \(4x^2-x-20=0\).
Answer
\(-5\).
Card 19 of 20
HardStudy card 19
Prompt
Why does a negative discriminant mean no horizontal-axis intersection?
Answer
The equation \(f(x)=0\) has no real input solutions.
Card 20 of 20
HardStudy card 20
Prompt
How do you validate quadratic-formula roots?
Answer
Substitute each branch into the original standard-form equation.
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