If the discriminant b^2-4ac is 0, then you have TWO EQUAL, REAL ROOTS.
If you're given the x-intercepts, you can determine the factors of the polynomial as follows: Take -3, change the sign and write (x+3). Take 5, change the sign and write (x-5). Then the eq'n of the parabola is
f(x) = (x+3)(x-5) = x^2 - 2x -15, in which a=1, b = -2 and c= -15.
You can find the x-coordinate of the vertex, which is also the equation of the axis of symmetry, using
x= -b / (2a). Here, x = -(-2) / (2[1]), or x = 1
Find the y-coordinate by subbing 1 for x in the equation above:
y = (1)^2 - 2(1) - 15 = 1 - 2 - 15 = -16
The vertex is at (1, -16) and the equation of the axis of symm. is x = 1.
The rate or slope is 2.15 $/gal
2.15 x 15 = 32.25
The percentage change is 36%
Answer:
20
Step-by-step explanation:
0 to 1 = a difference of 1
1 to 2 = a difference of 2-1 = 1
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2 to 4 = a difference of 2
4 to 6 = a difference of 2
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6 to 9 = a difference of 3
9 to 12 = a difference of 3
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12 to 16 = a difference of 4
16 to 20 = a difference of 4
If two secants are drawn from a point lying outside a circle, then the product of one secant on its outer part is equal to the product of the other secant on its outer part.
DE*CE = AE*BE
DE = CD + CE = 1 + x + 4 = x + 5
AE = AB + BE = 11 + x + 1 = x + 12
(x+5)(x+4)=(x+12)(x+1)
x² + 4x + 5x + 20 = x² + x + 12x + 12
9x + 20 = 13x + 12
20 - 12 = 13x - 9x
8 = 4x
x = 8/4
x = 2
