Final Exam Review Unit 3

Front

What is the equation of a parabola in vertex form?

Back

y = a(x - h)² + k, where (h, k) is the vertex.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: 1) If > 0, 2 real solutions; 2) If = 0, 1 real solution; 3) If < 0, 2 complex solutions.

Front

How do you find the discriminant of a quadratic equation?

Back

For ax² + bx + c = 0, the discriminant is calculated as b² - 4ac.

Front

What is the discriminant of the equation -2x² − x − 1 = 0?

Back

-7.

Front

If a function has a discriminant of -3, how many solutions does it have?

Back

2 Complex Solutions.

Front

Solve for m: 4m² + 10 = 38.

Back

m = √7, -√7.

Front

What is the vertex of the parabola given by y = (x + 2)² - 1?

Back

The vertex is (-2, -1).

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means the discriminant is less than zero, indicating complex solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If a > 0, it opens upwards; if a < 0, it opens downwards.