Hi

quadratic polynomial whose graph goes through the points (-1,5), (0,5), and (2,29). 

f(x) = ax^2 + bx + c

f(0) = 5 = c

f(x) = ax^2 + bx + 5   ****

a(-1)^2 + b(-1) + 5 = 5   ||  using (-1,5)

a*2^2  + 2b + 5 = 29      ||  using (2,29)

 a - b = 0

4a +2b = 24    ||multiplying 1st EQ thru by 2 and adding it to the second

  6a = 24

   a = 4  and b = 4   

 f(x) = 4x^2 + 4x + 5

 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 it's a quadratic polynomial and it goes through the points:

(-1,5)

(0,5)

(2,29)

the general form of a quadratic equation is:

ax^2 + bx + c = 0

another form of the quadratic equation is:

y = ax^2 + bx + c

if it goes through the point (-1,5), then this equation becomes:

5 = a(-1)^2 + b(-1) + c

simplify this to get:

5 = a - b + c

if it goes through the point (0,5), then this equation becomes:

5 = c

if it goes through the point (2,29), then this equation becomes:

29 = a(2)^2 + b(2) + c

simplify this to get:

29 = 4a + 2b + c

we have 3 equations:

they are:

5 = a - b + c

5 = c

29 = 4a + 2b + c

since c = 5, we can substitute in the other 2 equations to get:

5 = a - b + 5

29 = 4a + 2b + 5

these simplify to:

a - b = 0

4a + 2b = 24

a - b = 0 results in a = b

substitute a for b in the other equation to get:

4a + 2a = 24

simplify to get:

6a = 24

a = 4

we now know that a = 4 and c = 5

we also know that b = which results in b = 4

we should have:

a = 4

b = 4

c = 5

let's see if that works.

our equation is:

y = 4x^2 + 4x + 5

when x is equal to -1, we get:

y = 4(-1)^2 + 4(-1) + 5 which simplifies to:

y = 4 - 4 + 5 which results in y = 5 which is correct because we are dealing with the point (-1,5)

our equation is:

y = 4x^2 + 4x + 5

when x = 0, our equation becomes:

y = 0 + 0 + 5 which results in y = 5 which is correct because we are dealing with the point (0,5)

when x = 2, our equations becomes:

y = 4(2)^2 + 4(2) + 5 which simplifies to:

y = 16 + 8 + 5 which simplifies further to:

y = 29 which is correct because we are dealing with the point (2,29)

looks like we're good and the equation i:

y = 4x^2 + 4x + 5



 

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