Answer:
Two solutions
Step-by-step explanation:
This is a quadratic equation in the form y = ax² + bx + c.
For quadratic equations, you can find solutions using the quadratic formula:
[tex]x = \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex].
To find the number of solutions, you only need what's inside the square root. We call it the "discriminant" because lets us know the number of solutions without solving.
[tex]b^{2}-4ac[/tex]
If b²- 4ac > 0, two solutions. (greater than)
If b²- 4ac < 0, no solutions. (less than)
If b²- 4ac = 0, one solution. (equal to)
y = ax² + bx + c
y = -3x² + x + 12
a = -3 b = 1 c = 12
Substitute into the discriminant
b²- 4ac
= 1² - 4(-3)(12)
= 1 - (-144)
= 145 > 0
b²- 4ac > 0 Discriminant greater than 0
Therefore, there are two solutions.
