Answer:
(x+5)² = 16
Solution: -1 and -9
Step-by-step explanation:
Given the quadratic equation X^2+10x+22=13
Subtract 22 from both sides
X^2+10x+22-22=13-22
x^2+10x = -9
Complete the square
Add the square of half of coefficient of x to both sides
coefficient of x = 10
half of coefficient of x = 10/2 = 5
square of half of coefficient of x= 5² = 25
Add 25 to both sides
x²+10x + 25 = -9+25
(x+5)² = 16
Hence the required equation is (x+5)² = 16
(x+5)² = 16
square root both sides
√(x+5)² = √16
x+5 = √16
x +5 = ±4
x = +4 - 5 and -4-5
x = -1 and -9
Hence the solution to the equation is -1 and -9
Answer:
0
Step-by-step explanation
The company started off with $10 in the first section(quarter). They lost (subtract)$15 in the second section, In the third section they lost (subtract)$20. In the final section they gained (plus) a profit of $25.
10-15-20+25=0
The function is open up for both since the stretch value is positive. When opening you we don’t have a maximum value only a minimum value. So already we know B and d are wrong. When looking at minimums and maximums we look at the y or q value. In this case for f(x) it is 4 and for g(x) it is 5. So we know g(x) have a greater minimum value, so the answer is c
Thought you'd want to know: If you're talking about parabolas, it's parabolas, not probables. ;)
The standard equation of a a quadratic is y = ax^2 + bx + c. We need to find the values of the coefficients a, b and c.
Taking the first point: When x=3, y=0, so write 0 = a(3)^2 + b(3) + c, or
0 = 9a + 3b + 1c
Do the same for points (-2,3) and (-1,4).
You will have obtained three linear equations in a, b and c:
3= a(-2)^2 + b(-2) + c, or 3 = 4a - 2b + 1c, also
4 = a(-1)^2 + b(-1) + 1c, or 1a - 1b + 1c.
I used matrix operations to solve this system. The results are:
a= -2/5, b= 1/5, c= 21/5
and so the function f(x) is f(x) = (-2/5)x^2 + (1/5)x + 21/5.
