<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:
31.5 cubic feet
Step-by-step explanation:
the formula to find the volume of a rectangular prism is v = <em>whl</em>
w = width
h = height
l = length
(3.5)(2)(4.5) = 31.5
Answer:
x = - 
, x = 
Step-by-step explanation:
Given
x² - x - 
= 0 ( add to both sides )
x² - x =
Solve using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2( - )x + 
= +
(x - )² = 1 ( take the square root of both sides )
x - = ± 1 ( add to both sides )
x = ± 1
Thus
x = - 1 = -
x = + 1 =
Answer:
Price went up, $24.64/year for 28 years
Step-by-step explanation:
Change Year = 28
Change Price = 690
Average rate = 690/28 = 24.64
Answer: 1.86 repeating
Step-by-step explanation:
