Answer:
See below.
Step-by-step explanation:
Here's an example to illustrate the method:
f(x) = 3x^2 - 6x + 10
First divide the first 2 terms by the coefficient of x^2 , which is 3:
= 3(x^2 - 2x) + 10
Now divide the -2 ( in -2x) by 2 and write the x^2 - 2x in the form
(x - b/2)^2 - b/2)^2 (where b = 2) , which will be equal to x^2 - 2x in a different form.
= 3[ (x - 1)^2 - 1^2 ] + 10 (Note: we have to subtract the 1^2 because (x - 1)^2 = x^2 - 2x + 1^2 and we have to make it equal to x^2 - 2x)
= 3 [(x - 1)^2 -1 ] + 10
= 3(x - 1)^2 - 3 + 10
= <u>3(x - 1)^2 + 7 </u><------- Vertex form.
In general form the vertex form of:
ax^2 + bx + c = a [(x - b/2a)^2 - (b/2a)^2] + c .
This is not easy to commit to memory so I suggest the best way to do these conversions is to remember the general method.
Answer:1 1/6
Step-by-step explanation:
Answer:
A=32
B=3
C=7
Step-by-step explanation:
Caitlyn surveyed 100 students to find out their favorite class. There were 29 students who enjoyed biology and 35 students who enjoyed English. There were 12 students who did not enjoy Biology, English, or Math.
29 like Biology so to find B you subtract. 29-6-5=3
35 like English so to find C 35-3-5-20=7
Total of 100 students subtract what you know to find A.
100-15-6-5-3-7-20-12=32
