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What are the three forms of a quadratic?
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All Flashcards in Topic 2.6
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2.6.19 cards
What are the three forms of a quadratic?
Standard ax²+bx+c, factored a(x−p)(x−q), vertex a(x−h)²+k.
What does the sign of a tell you?
a > 0 opens up (minimum); a < 0 opens down (maximum).
Where is the y-intercept in standard form?
It's c — the constant term (set x = 0).
How do you get the x-intercepts from factored form?
Set each bracket to zero: a(x − p)(x − q) gives x = p and x = q.
What does vertex form reveal?
The turning point (h, k) and the max/min value k.
x-intercepts of y = (x − 4)(x + 1)?
x = 4 and x = −1 (watch the sign on (x + 1)).
Where is the axis of symmetry relative to the roots?
Exactly midway between the two x-intercepts.
What features do you need to sketch a quadratic?
Direction (sign of a), x-intercepts, y-intercept, and the vertex.
Which form is best for finding the roots?
Factored form, a(x − p)(x − q).
2.6.29 cards
Formula for the axis of symmetry?
x = −b/(2a) for y = ax² + bx + c — also midway between the x-intercepts.
What does completing the square give you?
Vertex form a(x − h)² + k, which shows the vertex (h, k) directly.
How do you complete the square on x² + bx + c?
Halve b, square it for the bracket (x + b/2)², then adjust the constant to keep it equal.
Where is the max/min value in vertex form?
It's k, reached at x = h: minimum if a > 0, maximum if a < 0.
Complete the square: x² − 6x + 11.
(x − 3)² + 2, so the vertex is (3, 2).
Vertex of y = a(x − h)² + k?
(h, k) — note (x − 3)² means h = +3.
How do you find a quadratic from its vertex and a point?
Write y = a(x − h)² + k, substitute the point to find a.
Minimum value vs minimum point?
Value = k (a number); point = (h, k) (coordinates).
Axis of symmetry of y = x² − 6x + 5?
x = −(−6)/(2·1) = 3.
2.6.36 cards
Where is the max/min value of a quadratic?
It's k in vertex form a(x − h)² + k: minimum if a > 0, maximum if a < 0, at x = h.
Range of a quadratic that opens up?
y ≥ k, where k is the vertex's y-value (the minimum).
Range of a quadratic that opens down?
y ≤ k, where k is the vertex's y-value (the maximum).
Range of f(x) = (x − 2)² + 3?
y ≥ 3 — opens up, vertex (2, 3).
Find the range from standard form ax² + bx + c?
Find the vertex (x = −b/(2a), then substitute), check the opening, then range is y ≥ k or y ≤ k.
Does the range boundary use h or k?
k (the y-value of the vertex). h is just where it occurs.
Topic 2.6 study notes
Full notes & explanations for Quadratic functions
Math AA exam skills
Paper structures, command terms & tips
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