For this parabola we have:
f ( 0 ) = 8
and : f ( 1 ) = 24
In the first equation ( A) :
f ( 0 ) = - 16 * ( 0 - 1 )² + 24 = - 16 * 1 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 - 1 )² + 24 = 24 ( correct )
For B:
f ( 0 ) = - 16 * ( 0 + 1 )² + 24 = - 16 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 + 1 )² + 24 = - 16 * 4 + 24 = - 64 + 24 = 40 ( false )
For C:
f ( 0 ) = - 16 * ( 0 - 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24 ( false )
For D:
f ( 0 ) = - 16 * ( 0 + 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24 ( false )
Answer:
A ) f ( t ) = - 16 * ( t - 1 )² + 24
ANSWER
EXPLANATION
We want to determine the value of f(3) that will lead to an average rate of change of 19 over the interval [3, 5].
The average rate of change of f(x) over the interval [a,b]:
If the average rate of change over the interval [3, 5] is 19, then;
From the to table f(5)=13
It says that b represents Becky’s score and c represents Cathy’s score.
Becky’s score was 5 less than Cathy’s score, its equation can be written as :-
b = c - 5
It says that their combined score totaled 185, its equation can be written as :-
b + c = 185
So, correct pair of equations is b = c - 5 and b + c = 185.
Across :
3. conclude
10. quantitative data
11. experiment
12. observe
down :
1. qualitative data
2. tentative
4. hypothesis
5. results
6. inference
7. analyze
8. data
9. variable
So we see the leading coefient is positive (the 3 in the 3x^2 is positive) so the paraobola opens upward
so for it to have 2 x intercepts, we must have the vertex below the x axis
we must have the y value of the vertex negative
so
a hack is this
to move a function up c units, add c to whole function
also
for
y=ax^2+bx+c
the x value of the vertex is -b/2a
the y value is found by subsituting that value for x
so
y=3x^2+7x+m
x value of vertex is
-7/(2*3)=-7/6
if we sub it in
y=3(-7/6)^2+7(-7/6)+m
y=49/12-49/6+m
we want the y value to be less than 0
so
0>49/12-49/6+m
0>49/12-98/12+m
0>-49/12+m
49/12>m
so it will have 2 x intercept for all m such that m<49/12
