If f(x) is a parabola with vertex (2,−1) whose equation isf(x) =ax2+bx+c, what are the values of a, b, c if the graph off inters
ects the y-axis at the point (0,3).
1 answer:
Answer:
(a, b, c) = (1, -4, 3)
Step-by-step explanation:
In vertex form, the equation is ...
... f(x) = a(x -2)² -1
This has a y-intercept of ...
... f(0) = a(0 -2)² -1 = 4a -1
We want that value to be 3, so we can find "a" as ...
... 4a -1 = 3 . . . . . set f(0) = 3
... 4a = 4 . . . . . . . add 1
... a = 1 . . . . . . . . divide by 4
Then ...
... f(x) = (x -2)² -1 = x² -4x +3
The coefficients are a=1, b=-4, c=3.
You might be interested in
Answer:
Step-by-step explanation:
step 1
Convert mixed number to an improper fraction
step 2
Using proportion
step 3
Convert to mixed number
The solution of the equation is and
Explanation:
The equations are and
First we shall solve the equation graphically.
The image of the graph is attached below.
This contains the solution to the system of equations.
The equations and
are plotted on the graph.
The intersection of these two equations are the solutions of the system of equations.
Thus, the intersection of the two equations are and
Now, we shall solve the equation algebraically.
Let us solve the equation using substitution method.
Let us substitute in
, we get,
Adding both sides by 2x, we have,
Adding both sides by 2, we get,
Dividing both sides by 3,
Thus, the value of x is 3.
Substituting in
, we get,
Thus, the value of y is 1.
Hence, The solution of the equation is and
Answer:
- 12 gallons 84%
- 8 gallons 4%
Step-by-step explanation:
I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.
Here, that means the ratio of 84% solution to 4% solution is ...
48 : 32 = 12 : 8
Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)
Mary must use ...
- 12 gallons of 84% acid solution
- 8 gallons of 4% acid solution
You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.
_____
<em>Check</em>
12 × 84% + 8 × 4% = 10.40 = 20 × 52%
_____
<em>Usual Solution</em>
A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...
0.84x + 0.04(20 -x) = 0.52(20)
0.80x + 0.8 = 10.4 . . . . simplify
0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8
x = 9.6/0.8 = 12 . . . . gallons of 84% acid
20-x = 8 . . . . . . . . . . gallons of 4% acid
