Answer:
y = -4x² + 32x - 48
Step-by-step explanation:
The standard form of a quadratic equation is
y = ax² + bx + c
We must find the equation that passes through the points:
(2, 0), (6,0), and (3, 12)
We can substitute these values and get three equations in three unknowns.
0 = a(2²) + b(2) + c
0 = a(6²) + b(6) + c
12 = a(3²) + b(3) + c
We can simplify these to get the system of equations:
(1) 0 = 4a + 2b + c
(2) 0 = 36a + 6b + c
(3) 12 = 9a + 3b + c
Eliminate c from equations (1) and (2). Subtract (1) from (2).
(4) 0 = 32a + 4b
Eliminate c from equations (2) and (3). Subtract (3) from (2).
(5) -12 = 27a - 3b
Simplify equations (4) and (5).
(6) 0 = 8a + b
(7) -4 = 9a - b
Eliminate b by adding equations (6) and (7).
(8) a = -4
Substitute (4) into (6).
0 = -32 + b
(9) b = 32
Substitute a and b into (1)
0 = 4(-4) + 2(32) + c
0 = -16 + 64 + c
0 = 48 + c
c = -48
The coefficients are
a= -4, b = 32, c = -48
The quadratic equation is
y = -4x² + 32x - 48
The diagram below shows the graph of your quadratic equation and the three points through which it passes.
Answer:
Write the following numbers in order from smallest value to largest value: 1.75, 1. Justify your answer. 4. If 2x2 – x + 6 is subtracted from x2 + 3x – 2, ...
Step-by-step explanation:
1. Which number is irrational?
(A) (B) (C) 0.3333 (D)
2. In which group are the numbers arranged in order from smallest value to largest value?
(A) π, 3.14, (B) 3.14, π
(C) , 3.14, π, (D) 3.14, , π,
3. Write the following numbers in order from smallest value to largest value:
1.75, 1
Justify your answer.
4. If 2x2 – x + 6 is subtracted from x2 + 3x – 2, the result is
(A) x2 + 2x – 8 (B) x2 – 4x + 8 (C) –x
2 + 2x – 8 (D) –x
2 + 4x – 8
Answer:
the bottom right graph represents a single function.
Step-by-step explanation:
Answer:
31.4 cm
Step-by-step explanation:
Let C be the circumference and r be the radius of the circle.
