Y= 12x2 - 9x + 4 how many real solution 10x + y = -x2 + 2 how many real solution(s) 4y - 7 = 5x2 - x + 2 + 3y how many real solution(s) y = (-x + 4)2 how many real solution(s)

(a) 0

(b) 2

(c) 0

(d) 1

Step-by-step explanation:

All of these can be solved easily by a graphing calculator. The attached graphs show the real solutions of those equations that have them. Here, you can also answer the question from the sign of the discriminant.

For y = ax² +bx +c

the value of the discriminant is

... b² -4ac

When the discriminant is negative, both solutions are complex. When 0, there is one solution. When positive, there are two real solutions.

(a) The discriminant is ...

... (-9)² -4(12)(4), a negative number. There are no real solutions.

(b) This needs to be rearranged to ...

... y = -x² -10x +2

Then the discriminant is ...

... (-10)² -4(-1)(2), a positive number. There are 2 real solutions.

(c) This needs to be rearranged to ...

... y = 5x² -x +9 . . . . add 7-3y

Then the discriminant is ...

... (-1)² -4(5)(9), a negative number. There are no real solutions.

(d) This equation is in vertex form, and the vertex is (4, 0). Since the vertex is the only x-intercept, there is one real solution.