The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the su
1 answer:
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Answer:
Intercept form is y= (x+5)(x+3)
vertex is (-4,1)
y intercept is (0,15)
x intercepts are (-5,0) (-3,0)
Step-by-step explanation:
Given quadratic function
To rewrite it in standard form we need to expand (x+4)^2
Intercept form is y=a(x-p)(x-q)
Factor x^2 + 8x + 15
product is 15 and sum is 8, 5*3= 15 and 5+3=8
(x+5)(x+3)
Intercept form is y= (x+5)(x+3)
Vertex form of equation is y=(x-h)^2+k
where (h,k) is the vertex
, here h = -4 and k =1 so vertex is (-4,1)
To find y intercept plug in 0 for x
y= (x+5)(x+3)
y= (0+5)(0+3) = 15, so y intercept is (0,15)
to find x intercept plug in 0 for y
y= (x+5)(x+3)
0= (x+5)(x+3), x+5 =0 and x+3=0
x=-5 and x= -3
So x intercepts are (-5,0) (-3,0)
Given
first, convert
to base 25 to match the other term.
Substitute above identity into original equation:
Use substiution
above equation becomes
2/u-3u=1
multiply by u and solve for u:
=> u=2/3 or u=-1
case A:. u=2/3 =>
=>
case B: u=-1 =>
which does not give a real solution, so reject.
See graph below for confirmation of solution.
first, convert
Substitute above identity into original equation:
Use substiution
above equation becomes
2/u-3u=1
multiply by u and solve for u:
=> u=2/3 or u=-1
case A:. u=2/3 =>
case B: u=-1 =>
which does not give a real solution, so reject.
See graph below for confirmation of solution.