Answer:
Step-by-step explanation:
1.Consider the quadratic relation y = x^2 – 6x – 16.
a) Factor this equation using the Trinomial Method (find two numbers that multiply to 'c' and add to 'b'; the factored form has 2 pairs of brackets).
[y = x^2 – 6x – 16 : Two numbers when multiplied = -16, but when added = -6, would be: -8 and 2. [-8+2 = -6, and -8*2 = -16] This would lead to (x+2)(x-8) as the two factors.
b) Find the x-intercepts (zeroes) of the relation. Remember to let y = 0 then solve for each x separately.
(x+2)=0; x= -2
(x-8)=0; x = 8
2. Consider the quadratic relation y = 2x^2 + 6x – 80.
a) Factor this equation by:
1. Determining the greatest common factor (GCF).
The GCF is 2: 2*(x^2 + 3x - 40)
2. Factoring the equation using common factoring.
2*(x^2 + 3x - 40): Two numbers that when multiplied = -40, but added = 3, would be 8 and -5. So we can factor:
2*(x + 8)(x - 5)
3. Factor the expression inside the brackets using the Trinomial Method (find two numbers that multiply to 'c' and add to 'b'; the factored form has 2 pairs of brackets).
2*(x + 8)(x - 5)
b) Find the x-intercepts (zeroes) of the relation. Remember to let y = 0 then solve for each x separately.
0 = (x + 8) and 0=(x - 5); x = -8, and x=5
