Three forms of a quadratic
SAT glossary · Course Foundations
Definition
Standard ax^2+bx+c gives the y-intercept c; vertex a(x-h)^2+k gives the vertex (h,k); factored a(x-r_1)(x-r_2) gives the roots. The form the test hands you is a hint about the quantity it wants, and none of this is on the reference sheet.
Three forms of a quadratic in plain English
A quadratic expression can be written in three completely different-looking (but mathematically equivalent) forms, and each one instantly reveals a different useful piece of information without any extra work: STANDARD form (ax^2+bx+c) directly shows you the y-intercept, which is just c. VERTEX form (a(x-h)^2+k) directly shows you the vertex point (h,k). FACTORED form (a(x-r_1)(x-r_2)) directly shows you the roots (x-intercepts), r_1 and r_2. Whichever form a question chooses to GIVE you is actually a strong hint about which piece of information it wants you to find — and none of this conversion knowledge is provided on the reference sheet, so it has to be memorized.
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