FLASHCARD: Solving Quadratics by Graphing and Factoring

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is expressed as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots (or x-intercepts) of the function.

Front

What are x-intercepts?

Back

X-intercepts are the points where a graph crosses the x-axis, meaning the output (y-value) is zero.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros, set the quadratic function equal to zero and solve for x.

Front

What does it mean for a quadratic function to have two zeros?

Back

It means the graph of the function intersects the x-axis at two distinct points.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How can you determine the number of zeros a quadratic function has?

Back

You can determine the number of zeros by calculating the discriminant (b² - 4ac) from the standard form. If it's positive, there are two zeros; if zero, one zero; if negative, no zeros.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of breaking down a quadratic equation into simpler binomial expressions that can be multiplied to give the original equation.

Front

Solve the quadratic by factoring: x² - 5x + 6 = 0.

Back

(x - 2)(x - 3) = 0; The solutions are x = 2 and x = 3.

Front

Find the zeros by factoring: h(x) = x² - 12x + 36.

Back

The zeros are (6, 0) only.