Question 761944: Please help me answer these following questions. These are part of the quadratic inequalities and i hope you can provide me with solutions along with the answers please so i may know how to deal with it on my own afterwards... So here they are:
1) For what values of x is the graph of y=4x - x^2 below the x-axis?
2) For what values of x is y negative if y=x^2 - 7x?
3) If 2x^2 +7x -30=0, find the value of 2x^2 +7x?
4) What is the smallest value of y= 2x^2 - 9x?
Please reply as soon as possible, thank you so much in advance!!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 1) For what values of x is the graph of y=4x - x^2 below the x-axis?
Find where the graph crosses the x-axis by setting y to zero and solving for x:
y=4x - x^2
0=4x - x^2
0=(x)(4 - x) factoring right side
setting each term (inside parentheses) to zero gives us:
x = {0, 4}
Answer: 0 <= x <= 4
.
2) For what values of x is y negative if y=x^2 - 7x?
since this is a "quadratic" (polynomial of degree two)
we know it is a parabola
because the coefficient associated with the x^2 is POSITIVE
we know the parabola opens upwards (happy face)
Therefore y is negative for the same range of values as part 1 above:
Answer: 0 <= x <= 4
.
3) If 2x^2 +7x -30=0, find the value of 2x^2 +7x?
we start with the given equation:
2x^2 +7x -30=0
now, we simply ADD 30 to both sides:
2x^2 +7x -30 + 30=0 +30
2x^2 +7x = 30
answer: 30
.
4) What is the smallest value of y= 2x^2 - 9x?
from part 2 we know that
y= 2x^2 - 9x
is a parabola that opens upwards.
Therefore the smallest value is the vertex.
Value of x at the vertex:
x = -b/(2a)
x = -(-9)/(2*2)
x = 9/4
Value of y, we plug above back into original equation:
y = 2(9/4)^2 - 9(9/4)
y = 2(81/16) - 81/4
y = 162/16 - 81/4
y = 162/16 - 324/16
y = (162 - 324)/16
y = -162/16
y = -81/4 (answer)
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