Answer:
a = -3/2 = -1.5
Step-by-step explanation:
(1+ax) (2+3x)³
Formula
(a+b)^3=a^3+3a^2b+3ab^2+b^3
(1 + ax) [ 2^3 + 3*2^2*3x + 3*2*(3x)^2 + (3x)^3]
(1 + ax) [ 8 + 12*3x + 6*9x^2 + 27x^3]
8 + 12*3x + <u>6*9x^2</u> + 27x^3 + 8ax + <u>36ax^2</u> + 54ax^3 + 27ax^4
coefficient of x^2 is zero
54x^2 + 36ax^2
54 + 36a = 0
36a = -54
a = -3/2
Format of Quadratic Equation: y = ax2 + bx + c
Given Quadratic Equation: y = 2x2 - 3x + 3
Coefficient Variable Values: a = 2 and b = -3 and c = 3
Axis of Symmetry: x = -b/2a = -(-3)/2(2) so answer is x = 3/4
Vertex: x value is axis of symmetry (3/4) and y value is calculated substituting 3/4 for x in original equation: y = 2(3/4)2 - 3(3/4) + 3 = 2(9/16) - 9/4 + 3 = 9/8 - 9/4 + 3 = 9/8 - 18/8 + 24/8 = 15/8,
so answer is (3/4,15/8)
x intercepts (solve using quadratic formula): x = (-b plus or minus sqrt(b2 - 4ac)/2a, so plugging in coefficient values for a and b and c, we get x = [-(-3) plus or minus sqrt((-3)2 - 4(2)(-3)]/2(2), which results in x = (3 + sqrt(33))/4 or (3 - sqrt(33))/4 and answers to nearest tenth are x = (3 + 5.7) / 4 = 2.2
or x = (3 - 5.7) / 4 = -0.7
y intercept is calculated by substituting zero for x into original equation: y = 2x2 - 3x + 3, so y-intercept is 3.
Domain is range is from calculated negative x intercept (-0.7) to calculated positive x intercept (2.2) and is written as (-0.7,2.2)
Range is from calculated y-intercept to positive infinity, since parabola opens up due to positive x2 coefficient value, so range is written as (3,positive infinity). Note: infinity symbol is sideways 8.
Answer:
the answer is 5^2
Step-by-step explanation:
TURTLES AREN'T GREEN?!?!?!?
Answer: it’s the first 1
Step-by-step explanation:
