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Flip to reveal answersWhat are the three forms of a quadratic?
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All 9 Flashcards — Quadratic graphs
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Question
What are the three forms of a quadratic?
Answer
Standard ax²+bx+c, factored a(x−p)(x−q), vertex a(x−h)²+k.
Question
What does the sign of a tell you?
Answer
a > 0 opens up (minimum); a < 0 opens down (maximum).
Question
Where is the y-intercept in standard form?
Answer
It's c — the constant term (set x = 0).
Question
How do you get the x-intercepts from factored form?
Answer
Set each bracket to zero: a(x − p)(x − q) gives x = p and x = q.
Question
What does vertex form reveal?
Answer
The turning point (h, k) and the max/min value k.
Question
x-intercepts of y = (x − 4)(x + 1)?
Answer
x = 4 and x = −1 (watch the sign on (x + 1)).
Question
Where is the axis of symmetry relative to the roots?
Answer
Exactly midway between the two x-intercepts.
Question
What features do you need to sketch a quadratic?
Answer
Direction (sign of a), x-intercepts, y-intercept, and the vertex.
Question
Which form is best for finding the roots?
Answer
Factored form, a(x − p)(x − q).
Read the notes
Full study notes for Quadratic graphs
Topic 2.6 hub
Quadratic functions
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Math AA SL exam skills
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