Card 1 of 20
EasyStudy card 1
Prompt
What is the standard form of a quadratic function?
Answer
\(f(x)=ax^2+bx+c\), where \(a\ne0\).
MathChapter 11: Quadratic Functions
Flashcards
Graphs of Quadratic Equations Flashcards
Twenty recall-focused cards on quadratic forms, vertices, symmetry, and intercepts.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is the graph of a quadratic function called?
Answer
A parabola.
Card 3 of 20
EasyStudy card 3
Prompt
What does \(a>0\) tell you about a parabola?
Answer
It opens upward, so its vertex is a minimum.
Card 4 of 20
EasyStudy card 4
Prompt
What does \(a<0\) tell you about a parabola?
Answer
It opens downward, so its vertex is a maximum.
Card 5 of 20
EasyStudy card 5
Prompt
What is the symmetry-axis formula for \(ax^2+bx+c\)?
Answer
\(x=-\frac{b}{2a}\).
Card 6 of 20
EasyStudy card 6
Prompt
How do you find the vertex after finding its horizontal coordinate \(h\)?
Answer
Evaluate \(k=f(h)\); the vertex is \((h,k)\).
Card 7 of 20
EasyStudy card 7
Prompt
What does vertex form reveal immediately?
Answer
From \(a(x-h)^2+k\), the vertex is \((h,k)\).
Card 8 of 20
MediumStudy card 8
Prompt
What does factored form reveal immediately?
Answer
From \(a(x-r_1)(x-r_2)\), the real roots are \(r_1\) and \(r_2\).
Card 9 of 20
MediumStudy card 9
Prompt
What does the constant \(c\) reveal in standard form?
Answer
The vertical-axis intercept is \((0,c)\).
Card 10 of 20
MediumStudy card 10
Prompt
How are roots, zeros, and horizontal-axis intercepts related?
Answer
They are the input values satisfying \(f(x)=0\).
Card 11 of 20
MediumStudy card 11
Prompt
How many real roots can a quadratic have?
Answer
Zero, one repeated root, or two distinct roots.
Card 12 of 20
MediumStudy card 12
Prompt
How is the symmetry axis related to two real roots?
Answer
Its coordinate is their average: \(h=\frac{r_1+r_2}{2}\).
Card 13 of 20
MediumStudy card 13
Prompt
What is the sign trap in \(a(x-h)^2+k\)?
Answer
The visible sign inside the parentheses is opposite the sign of \(h\).
Card 14 of 20
MediumStudy card 14
Prompt
Does upward opening mean every output is positive?
Answer
No. It only means the vertex is a minimum.
Card 15 of 20
MediumStudy card 15
Prompt
Which form is usually best for reading a maximum or minimum?
Answer
Vertex form, because it exposes \((h,k)\).
Card 16 of 20
MediumStudy card 16
Prompt
Which form is usually best for reading real roots?
Answer
Factored form, because each factor can be set equal to zero.
Card 17 of 20
HardStudy card 17
Prompt
Find the symmetry axis for roots \(-3\) and \(9\).
Answer
\(x=3\), because \(\frac{-3+9}{2}=3\).
Card 18 of 20
HardStudy card 18
Prompt
What is the vertex of \(2(x+4)^2-7\)?
Answer
\((-4,-7)\).
Card 19 of 20
HardStudy card 19
Prompt
How can you verify a labeled graph point?
Answer
Substitute its horizontal coordinate into the equation and confirm the output coordinate.
Card 20 of 20
HardStudy card 20
Prompt
What must agree when three forms describe one quadratic?
Answer
Their expanded coefficients, vertex, roots where real, and intercepts must describe the same graph.
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