6)
A quadratic function has the form
y = ax^2 + bx + c
Use point (3, 5) in the equation above:
5 = a(3^2) + 3b + c
5 = 9a + 3b + c
9a + 3b + c = 5 Equation 1
Use point (4, 3) in the equation above:
3 = a(4^2) + 4b + c
16a + 4b + c = 3 Equation 2
Use point (5, 3) in the equation above.
5 = a(5^2) + 5b + c
25a + 5b + c = 5 Equation 3.
Now solve the system of equations of equations 1, 2, and 3 to find the coefficients, a, b, and c.
9a + 3b + c = 5
16a + 4b + c = 3
25a + 5b + c = 5
Subtract the first equation from the second equation.
Subtract the second equation from the third equation.
You get
7a + b = -2
9a + b = 2
Subtract the first equation above from the second equation to get.
2a = 4
a = 2
Substitute:
7a + b = -2
7(2) + b = -2
b = -16
9a + 3b + c = 5
9(2) + 3(-16) + c = 5
18 - 48 + c = 5
c - 30 = 5
c = 35
The equation in standard form is
y = 2x^2 - 16x + 35
We can find it in vertex form:
y = 2(x^2 - 8x) + 35
y = 2(x^2 - 8x + 16) + 35 - 32
y = 2(x - 4)^2 + 3
Since z is proportion to the x
z = a x
190 = a 10
a = 19
when x = 13
z = a x
z = 19 * 13
z = 247
X intercept: y = 0
y= -3/4x -4
0 = -3/4 x - 4
4= -3/4 x
4 • -4/3 = x
-5.3 = x
y intercept: x = 0
y = -3/4 x -4
y = -3/4 (0) -4
y = -4
the points are (-5.3, 0) and (0, -4)
Answer:
Money Ivan gets extra = 120 - 30 (or 3x) = 90
Step-by-step explanation:
Ivan = 4x
Tanya = 1x
Total = 150
4x + x = 150
5x = 150 ; x = 150 / 5 = 30
Ivan = 4x = 120
Tanya = 1x = 30
Money Ivan gets extra = 120 - 30 (or 3x) = 90
(n + 7)2 = n - 1
2n +14 = n - 1
2n - n +14 = n - n - 1
n + 14 -14 = -1 - 14
n = -15
(-15 + 7)2 = -15 - 1
(-8)2 = -16
-16 = -16
