EmSAT Mathematics Flashcards

What is the quadratic formula?

Answer: x = −b ± √(b²−4ac) / 2a

The quadratic formula is x = [−b ± √(b²−4ac)] / 2a. It solves ax² + bx + c = 0 for x.

Solve: x² − 5x + 6 = 0

Answer: x = 2 or x = 3

Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.

What is the discriminant of x² + 4x + 5 = 0?

Answer: −4

Discriminant = b² − 4ac = 4² − 4(1)(5) = 16 − 20 = −4. A negative discriminant means no real roots.

What type of roots does a quadratic have if the discriminant is negative?

Answer: Two complex roots

When the discriminant (b² − 4ac) is negative, the square root of a negative number gives imaginary numbers, resulting in two complex (non-real) roots.

Expand: (x + 3)²

Answer: x² + 6x + 9

(x + 3)² = (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9. Remember the middle term 2(x)(3) = 6x.

If the graph of y = ax² opens downward, what can you say about a?

Answer: a < 0

In y = ax², when a > 0 the parabola opens upward, and when a < 0 it opens downward. A negative coefficient causes the downward opening.