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F(x) = -x^2 - 4x + 5
This is a quadratic function of the form y = ax + by + c, whose graph is a parabola. So,
a = -1, b = -4 and c = 5
Since a is negative the parabola opens downward, and the maximum valy of the function is equal to the value of the y-coordinate of the vertex.
The x- coordinate of the vertex is x = -b/2a. So,
x = -(-4)/[2(-1) = 4/-2 = -2 When x = -2, then
y = -(-2)^2 - 4(-2) + 5 = -4 + 8 + 5 = 9
Thus, the range is all value of y, such that y ≤ 9, Equivalently, the range is {y| y ≤ 9} or
[9, ∞).
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How do you factor 16x2 plus 40x plus 25?
16x2 + 40x + 25 = 16x2 + 20x + 20x + 25 = 4x(4x + 5) + 5(4x + 5) = (4x + 5)(4x + 5) = (4x + 5)2
How do you factor x squared minus 4x minus 5?
Find factors of -5 that can be added to make -4, in this case -5 and 1, so: (x - 5)(x + 1) = x2 - 4x - 5
Factor completely 8x squared plus 6x minus 5?
8x^2 + 6x - 5 = 8x^2 + 10x - 4x - 5 = 2x * (4x + 5) - (4x + 5) = (2x -1) * (4x + 5)
Find area of room?
Find the area of a floor with width 4x+2 and length 3x-5
What is the solution to 4x squared minus x minus 5 equals 0?
4x2 - x - 5 = 0 4x2 + 4x - 5x - 5 = 0 4x(x + 1) - 5(x + 1) = 0 (4x - 5)(x + 1) = 0 4x - 5 = 0 or x + 1 = 0 4x = 5 or x = -1 x = 5/4 o x = -1
What is the answer to 8x-5 equals 23 plus 4x?
8x-5=23+4x 8x-5-4x=23+4x-4x 4x-5=23 4x-5+5=23+5 4x=28 4x/4=28/4 x=7
Factor 16x2 - 25?
16x2 - 25 = (4x + 5) ( 4x - 5)
Factor the polynomial expression 16x2 - 25?
16x2 - 25 = (4x + 5) (4x - 5)
How do you factor 16x2 plus 40x plus 25?
16x2 + 40x + 25 = 16x2 + 20x + 20x + 25 = 4x(4x + 5) + 5(4x + 5) = (4x + 5)(4x + 5) = (4x + 5)2
How does you solve 4x plus 5 equals 8?
4x+5 = 8 Subtract 5 from both sides: 4x = 3 Divide both sides by 4 to find the value of x: x = 3/4 or 0.75
Find the value of x: 2(4x + 4) = (4x - 12)?
2(4x + 4) = (4x - 12) 8x + 8 = 4x - 12 8x - 4x + 8 = 4x - 4x - 12 4x + 8 = -12 4x + 8 - 8 = -12 - 8 4x = -20 4x/4 = -20/4 x = -5
4x plus 5 equals -9?
4x+5 = -9 4x = -9-5 4x = -14 x = -3.5
How do you factor x squared minus 4x minus 5?
Find factors of -5 that can be added to make -4, in this case -5 and 1, so: (x - 5)(x + 1) = x2 - 4x - 5
What is 4x equals 20?
4x = 20 x = 5 (divide both sides by 4)
What is the answer to 4x-3 equals 5?
4x - 3 = 5 4x = 5 + 3 4x = 8 x = 8/4 x = 2
An angle measures 5 degrees more than 4 times its compliment find the measure of the angle?
measure of angle = 73 work x = angle (90 - x) = complement x = 4 (90 - x) + 5 x = 360 - 4x + 5 x = 365 - 4x x + 4x = 365 - 4x + 4x 5x = 365 5x / 5 = 365 / 5 x = 73
Factor completely 8x squared plus 6x minus 5?
8x^2 + 6x - 5 = 8x^2 + 10x - 4x - 5 = 2x * (4x + 5) - (4x + 5) = (2x -1) * (4x + 5)
