To determine how far the firework will travel before it reaches the ground, we need to solve the equation:
0 = -x^2 + 15x
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring the equation, we have:
0 = -x(x - 15)
Setting each factor equal to zero, we get:
x = 0 or x - 15 = 0
From the first factor, x = 0 does not make sense in this context as it represents the starting point of the firework. From the second factor, x - 15 = 0, we find:
x = 15
Therefore, the firework will travel 15 feet before it reaches the ground.
As Isla prepares to set off fireworks, she wants to ensure the spectators are a safe distance away. When shot in the air, one firework will follow the path h(x)=−x2+15x , where h(x) is the height of the firework, and x is the horizontal distance it travels in feet. To determine how far the firework will travel before it reaches the ground, Isla sets the height equal to zero, and solves the following quadratic equation: 0=−x2+15x . How far will the firework travel before it reaches the ground?(1 point) Responses −15 feet negative 15 feet 30 feet 30 feet 7.5 feet 7.5 feet 15 feet 15 feet
5 answers
Hyung-eun is solving the quadratic equation x2−4x−12=0 by grouping. Her work is shown below. At which step does Hyung-eun first make an error? x2−4x−12=0 Step1: x2+(−6x)+2x−12=0 Step 2: (x2+(−6x))+(2x−12)=0 Step 3: x(x+(−6))+2(x−6)=0 x(x−6)+2(x−6)=0 Step 4: (x+6)(x−2)=0 Step 5: x+6=0 or x−2=0 x=−6 or x=2 (1 point) Responses Step 1 Step 1 Step 2 Step 2 Step 4 Step 4 Step 3
Hyung-eun first makes an error in Step 3.
In Step 3, she distributes the 2 to both terms in parentheses correctly, but when she combines like terms, she incorrectly writes "2(x-6)" as "2(x-6)" instead of "2(x-6)".
The correct step should be:
x(x-6) + 2(x-6) = 0
Therefore, the error occurs in Step 3.
In Step 3, she distributes the 2 to both terms in parentheses correctly, but when she combines like terms, she incorrectly writes "2(x-6)" as "2(x-6)" instead of "2(x-6)".
The correct step should be:
x(x-6) + 2(x-6) = 0
Therefore, the error occurs in Step 3.
Which of the following quadratic equations can be solved by grouping?(1 point) Responses x2−4x−8=0 x squared minus 4 x minus 8 equals 0 x2+8x−22=0 x squared plus 8 x minus 22 equals 0 x2−12x+18=0 x squared minus 12 x plus 18 equals 0 x2+10x+21=0
The quadratic equation that can be solved by grouping is:
x2−4x−8=0
(x squared minus 4x minus 8 equals 0)
Solving this equation using grouping can involve breaking the middle term (-4x) into two terms that can be grouped and factored.
x2−4x−8=0
(x squared minus 4x minus 8 equals 0)
Solving this equation using grouping can involve breaking the middle term (-4x) into two terms that can be grouped and factored.
1 answer