Because quadratic functions are simpler versions of general polynomial functions, graph as parabolic curves, and are featured in many real-world situations, this subtopic holds a prominent place in the syllabus.
Following is a list of concepts you should firmly understand before taking the SAT/ACT.
-
[Note: “iff” means “if and only if.”]
Definition
Quadratic functions: functions involving one first-degree variable and one second degree variable (typically y^1 and x^2).
Quadratic Function Standard Form
y = ax^2+bx+c.
Parabola
Vertex = (h,k) with h = -b/2a, k = f(h).
Axis: x = h.
y-intercept = c.
Vertex Form
y = a(x–h)^2+k.
Vertex = (h,k).
Radius = r.
Discriminant
D = sqrt(b^2–4ac).
D > 0 iff 2 real solutions.
D = 0 iff 1 real solution.
D < 0 iff no solutions.
Sum and Product Formula
x^2–(sum)x+(prod) = 0.
-
For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this important material.
Following is a list of concepts you should firmly understand before taking the SAT/ACT.
-
[Note: “iff” means “if and only if.”]
Definition
Quadratic functions: functions involving one first-degree variable and one second degree variable (typically y^1 and x^2).
Quadratic Function Standard Form
y = ax^2+bx+c.
Parabola
Vertex = (h,k) with h = -b/2a, k = f(h).
Axis: x = h.
y-intercept = c.
Vertex Form
y = a(x–h)^2+k.
Vertex = (h,k).
Radius = r.
Discriminant
D = sqrt(b^2–4ac).
D > 0 iff 2 real solutions.
D = 0 iff 1 real solution.
D < 0 iff no solutions.
Sum and Product Formula
x^2–(sum)x+(prod) = 0.
-
For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this important material.
-----
Copyright © 2006-present: Christopher R. Borland. All rights reserved.
No comments:
Post a Comment