Answer: x² + 2y - 20x = 0
Step-by-step explanation:
Vertex form of the equation: y = a(x - h)² + k where (h, k) is the vertex and "a" is the vertical stretch.
Firework #1 has a vertex of (10, 50) and another coordinate of (0,0).
0 = a(0 - 10)² + 50
0 = a(100) + 50
-50 = 100a
[tex]-\frac{1}{2}[/tex] = a
Equation: y = [tex]-\frac{1}{2}[/tex](x - 10)² + 50
General form is when
- everything is on one side and zero on the other
- all expressions are expanded
- x is a positive integer
(-2)y = (-2)[tex]-\frac{1}{2}[/tex](x - 10)² + (-2)50
-2y = (x - 10)² - 100
-2y = (x² - 20x + 100) - 100
0 = x² + 2y - 20x
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Answer: y = [tex]-\frac{1}{2}[/tex](x - 10)² + 72
Step-by-step explanation:
Vertex form of the equation: y = a(x - h)² + k where (h, k) is the vertex and "a" is the vertical stretch.
Firework #2 has a vertex of (10, 72) and another coordinate of (22,0).
0 = a(22 - 10)² + 72
0 = a(12)² + 72
0 = 144a + 72
-72 = 144a
[tex]-\frac{1}{2}[/tex] = a
Equation: y = [tex]-\frac{1}{2}[/tex](x - 10)² + 72
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Answer: Domain: 0 ≤ x ≤ 22 [0, 22]
Range: 0 ≤ y ≤ 50 [0, 50]
Step-by-step explanation:
Domain represents the values of x. The x-values for Fireworks #1 graph are inclusively between 0 and 22.
Range represents the values of y. The y-values for Fireworks #1 graph are inclusively between 0 and 50.
