Write y = x2 + 2x - 6 in vertex form.
2 answers:
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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:
.
To find the number of solutions, <u>you only need what's inside the square root</u>. We call it the "<u>discriminant</u>" because lets us know the number of solutions without solving.
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
<u>Substitute into the discriminant</u>
b²- 4ac
= 1² - 4(-3)(12)
= 1 - (-144)
= 145 > 0
b²- 4ac > 0 Discriminant greater than 0
Therefore, there are two solutions.