Question

Complete the standard form equation representing the quadratic relationship displayed above, where a,b, and c are consonants.

Answer 1

Explanation:

standard equation would be

y = ax² + bx + c

out of that we know already from (0, 5) that c = 5, as

a×0² + b×0 + c = 5.

because of (-1, -5) we see

-5 = a×1 + b×-1 + 5 = a - b + 5

-10 = a - b

or

a = b - 10

because of (1, 11) we see

11 = a×1 + b×1 + 5 = a + b + 5

6 = a + b

now we use the previous equation :

6 = (b - 10) + b = 2b - 10

16 = 2b

b = 8

.

a = b - 10 = 8 - 10 = -2

so, our standard equation is

y = -2x² + 8x + 5

Answer 2

y = - 2x² + 8x + 5

Explanation:

the equation of a quadratic function in standard form is

y = ax² + bx + c ( a ≠ 0 )

to find a, b and c use ordered pairs from the table

(0, 5 )

5 = a(0)² + b(0) + c = 0 + 0 + c = 5 ⇒ c = 5 , then

y = ax² + bx + 5

(1, 11 )

11 = a(1)² + b(1) + 5 = a + b + 5 ( subtract 5 from both sides )

a + b = 6 → (1)

(2, 13 )

13 = a(2)² + b(2) + 5 = 4a + 2b + 5 ( subtract 5 from both sides )

4a + 2b = 8 → (2)

solve the 2 equations simultaneously to find a and b

multiplying (1) by - 2 and adding to (2) will eliminate b

- 2a - 2b = - 12 → (3)

add (2) and (3) term by term to eliminate b

2a + 0 = - 4

2a = - 4 ( divide both sides by 2 )

a = - 2

substitute a = - 2 into (1) and solve for b

- 2 + b = 6 ( add 2 to both sides )

b = 8

then a = - 2, b = 8 and c = 5 gives the standard quadratic function

y = - 2x² + 8x + 5