Expand if necessary combine like terms
(5x+1) (5x-1)=
This is the quadratic function:
h(x)=ax²+bx+c
We have two points:
(1,58)
(2,112)
Now, we calculate this quadratic funtion.
we assume that h(0)=0
Therefore:
a(0)²+b(0)+c=0
c=0
(1,58)
a(1)²+b(1)=58
a+b=58 (1)
(2,112)
a(2)²+b(2)=112
4a+2b=112
2a+b=56 (1)
With the equations (1) and (2) we make a system of equations:
a+b=58
2a+b=56
we can solve this system of equations by reduction method.
-(a+b=58)
2a+b=56
---------------------
a=-2
-2(a+b=58)
2a+b=56
-------------------
-b=-60 ⇒ b=60
The function is:
h(x)=ax²+bx+c
h(x)=-2x²+60x
Now find the height, in feet, of the rock after 10 seconds in the air.
h(10)=-2(10)²+60(10)
h(10)=-200+600=400
Answer: 400 ft.
Answer:
4 3/11
Step-by-step explanation:
Find the function of the first two points
slope = delta y/delta x
slope = y1-y2/x1-x2
slope = (11-(-1))/(-10-1)
slope = 12/-11
Find the y intercept
y=(-12/11)x+b
-1 = (-12/11)*-1+b
-1 = 12/11+b
-23/11=b
y=(-12/11)x-23/11
Plug in x to find y
y=(-12/11)2-23/11
y=
4 3/11
<h2>Answer: y = - x + 1
</h2>
<h3>Step-by-step explanation:
</h3>
For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:
The question gives us two points, (-3, 4) and (2, -1), from which we can find the slope and later the equation of the line.
<u>Finding the Slope</u>
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (4 - (- 1)) ÷ ((-3) - 2)
= - 1
<u>Finding the Equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-1) = - 1 (x - 2)
y + 1 = - (x - 2)
we could also transform this into the slope-intercept form ( y = mx + c) by making y the subject of the equation:
since y + 1 = - (x - 2)
∴ y = - x + 1
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>