Answer:
1. It has two points in common with the x-axis.
2. The vertex in relation to the x-axis is at 
Step-by-step explanation:
The points that the equation has in common with the x-axis are the points of intersection of the parabola with the x-axis.
To find them, substitute y=0 and solve for "x":
Use the Quadratic formula:
It has two points in common with the x-axis.
To find the vertex in relation to the x-axis, use the formula:
Substituting values, you get:
Answer:
56
Step-by-step explanation:
Multiply -8 on both sides and k = 56
Answer:
Step-by-step explanation:
The given quadratic expression is
3x² - 9x + 6
Dividing each term in the expression by 3 in order to simplify it further, it becomes
x² - 3x + 2 = 0
We would determine two numbers such that their sum or difference is -3x and their product is 2x².
The two numbers are - 2x and - x.
Therefore,
x² - 2x - x + 2
x(x - 2) - 1(x - 2)
(x - 1)(x - 2)
When the expression is factored completely, it is equivalent to
(x - 1)(x - 2)
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
It would be: 18/15 * 100 = 1800/15 = 120%
