Parabolas: Vertex, Intercepts, and Form
Key facts about the three forms of a quadratic and how to read a parabola's features.
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Questions Covered in This Set
10 cards to master
Standard form of a quadratic and what it reveals
y = ax² + bx + c → reveals the y-intercept (0, c)
Factored form and what it reveals
y = a(x − p)(x − q) → reveals the x-intercepts (p, 0) and (q, 0)
Vertex form and what it reveals
y = a(x − h)² + k → reveals the vertex (h, k)
Vertex of y = 2(x + 3)² − 5
(−3, −5) — opposite of what's inside, same as what's outside
What does the sign of a tell you?
a > 0 opens up (vertex is a minimum); a < 0 opens down (vertex is a maximum). Bigger |a| = narrower.
Axis of symmetry formula
x = −b/(2a); plug it back in to get the vertex y-value
Midpoint trick for the vertex
The vertex x-value is halfway between the x-intercepts: x = (p + q)/2
Discriminant and number of x-intercepts
b² − 4ac: positive → 2 intercepts, zero → 1, negative → 0
Complete the square: y = x² − 6x + 8
Half of −6 is −3, squared is 9: y = (x − 3)² − 1, vertex (3, −1)
Maximum height of h(t) = −16t² + 64t + 5
t = −64/(2·−16) = 2 s; h(2) = 69 feet (and +5 is the starting height)
