Solving Quadratic Equations Flashcard #6 Review

Front

What is the first step to solving the equation a² + 10a + 21 = 0 by completing the square?

Back

Subtract the 21.

Front

Is x² + 10x + 25 a perfect square trinomial?

Back

Yes.

Front

For the function graphed, what is the solution if it does not intersect the x-axis?

Back

No solution.

Front

Solve using square roots: 5b² - 4 = 41. What are the values of b?

Back

b = 3, b = -3.

Front

Complete the square for the equation x² + 6x = 5. What is the result?

Back

(x + 3)² = 14.

Front

What is a perfect square trinomial?

Back

A trinomial that can be expressed as the square of a binomial, e.g., (x + a)² = x² + 2ax + a².

Front

What does it mean to complete the square?

Back

To transform a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you determine if a quadratic equation has real solutions?

Back

By calculating the discriminant (b² - 4ac); if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is the vertex form of a quadratic equation?

Back

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