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:
= 8.25
Step-by-step explanation:
6, 8, 8.5, 11
The middle number are 8 and 8.5
We then add them and divide by 2
= 8 + 8.5 / 2
= 16.5/2
= 8.25
Answer:
2916π in^2
Step-by-step explanation:
Step one:
given data
initial table diamter= 96in
we are told that the extension is 6 in over the edge
the new diameter is = 96+6+6= 108in
the radius is = 108/2=54in
we added 6 twice because it will be on the two sides of the diameter
Step two:
the expression for the area is
Area= πr^2
Area= π*54^2
Area= 2916π in^2
<h3>
Answer: 40 novels</h3>
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Work Shown:
n = number of novels
(32 ebooks)/(n novels) = 4/5
32/n = 4/5
32*5 = n*4 ............ cross multiply
160 = 4n
4n = 160
n = 160/4 .............. dividing both sides by 4
n = 40
There are 40 novels.
Answer: f(2)=7
Step-by-step explanation:
F(2)= 4x2^2-5x2+1
4x4-10+1
6+1=7
