Solving Quadratic Equations Mixed Review

Front

What is the first step in solving a quadratic equation using the factoring method?

Back

Make it equal 0 by moving all terms to one side of the equation.

Front

What are the roots of the equation k² − 12k + 23 = 0?

Back

The roots are 6 + √13 and 6 - √13.

Front

How do you solve the equation x² = 7x + 18 by factoring?

Back

Rearrange to x² - 7x - 18 = 0, then factor to (x - 9)(x + 2) = 0, giving roots 9 and -2.

Front

What is the Square Root method used for in solving quadratic equations?

Back

It is used to solve equations of the form ax² = c by isolating x² and taking the square root of both sides.

Front

What is the first step in completing the square for the equation a² + 10a + 21 = 0?

Back

Subtract 21 from both sides to isolate the quadratic and linear terms.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What does it mean for a quadratic equation to have real roots?

Back

It means that the solutions to the equation are real numbers, which occurs when the discriminant (b² - 4ac) is non-negative.

Front

What is the discriminant in a quadratic equation and how is it used?

Back

The discriminant is b² - 4ac; it determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

If the coefficient 'a' in ax² + bx + c is positive, the parabola opens upwards; if negative, it opens downwards.