<span>5.1 </span> Find the Vertex of <span>y = x2-2x-15
</span>Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).<span>
</span>Each
parabola has a vertical line of symmetry that passes through its
vertex. Because of this symmetry, the line of symmetry would, for
example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.<span>
</span>Parabolas
can model many real life situations, such as the height above ground,
of an object thrown upward, after some period of time. The vertex of the
parabola can provide us with information, such as the maximum height
that object, thrown upwards, can reach. For this reason we want to be
able to find the coordinates of the vertex.<span>
</span>For any parabola,<span>Ax2+Bx+C,</span>the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 1.0000 <span>
</span>Plugging into the parabola formula 1.0000 for x we can calculate the y -coordinate :<span>
</span><span> y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 15.0
</span> or <span> y = -16.000</span>
Answer:
Step-by-step explanation:
-2x - 6 = 2 - 4x - x + 1
-2x - 6 = 3 - 5x
3x - 6 = 3
3x = 9
x = 3
Step-by-step explanation:
the range is the biggest number subtracted by the smallest 23-(-11)= 34
Answer:
The length of the edge of the cube = 4 inches
Step-by-step explanation:
* Lets describe the cube
- It has 6 faces all of them are squares
- It has 8 vertices
- It has 12 equal edges
∵ The volume of any formal solid = area of the base × height
∵ The base of the cube is a square
∴ Area base = L × L = L² ⇒ L is the length of the edge of it
∵ All edges are equal in length
∴ Its height = L
∴ The volume of the cube = L² × L = L³
* Now we have the volume and we want to find the
length of the edges
∵ Its volume = 64 inches³
∴ 64 = L³
* Take cube root to the both sides
∴ ∛64 = ∛(L³)
∴ L = 4 inches
* The length of the edge of the cube = 4 inches
7x+3y=33 3x+y=8
X represents bottles of ketchup and Y mustard
