Answer:
Vertex form: f(x) = -10(x − 2)^2 + 3
Standard form: y = -10x^2 + 40x - 37
Step-by-step explanation:
h and k are the vertex coordinates
Substitute them in the vertex form equation:
f(x) = a(x − 2)^2 + 3
Calculate "a" by replacing "f(x)" with -7 and "x" with 1:
-7 = a(1 − 2)^2 + 3
Simplify:
-7 = a(1 − 2)^2 + 3
-7 = a(-1)^2 + 3
-7 = a + 3
-10 = a
Replace a to get the final vertex form equation:
f(x) = -10(x − 2)^2 + 3
Convert to standard form:
y = -10(x − 2)^2 + 3
Expand using binomial theorem:
y = -10(x^2 − 4x + 4) + 3
Simplify:
y = -10x^2 + 40x - 40 + 3
y = -10x^2 + 40x - 37
When two variables have a positive linear correlation, the dependent variable increases as the independent variable increases. So when the independent variable decreases, the dependent variable decreases as well. Both variables decrease and increase simultaneously.
1. The segment LO bisects one of the angles of the triangle shown in the figure attached, and divide the segment NM in two segments: NO and OM. Therefore, you must apply the Triangle Angle Bisector Theorem, which is shown below:
LN/LM=NO/OM
LN=10
LM=18
NO=4
OM=x (The value you want to find)
2. When you substitute this values in LN/LM=NO/OM, you have:
10/18=4/x
10x=(18)(4)
x=(18)(4)/10
x=72/10
3. Finally, you obtain:
x=7.2
The answer is: The value of "x" is 7.2
