5.1.3 Finding Zeros and X-Intercepts (factored form)

Front

What does it mean to 'find the zeros' of a quadratic?

Back

To find the zeros of a quadratic means to factor the quadratic expression, set each factor equal to zero, and solve for the values of x that make the equation true.

Front

How do you solve the equation (x - 5)(x - 1) = 0?

Back

Set each factor equal to zero: x - 5 = 0 gives x = 5, and x - 1 = 0 gives x = 1. Therefore, the solutions are (5, 0) and (1, 0).

Front

What is another term for 'x-intercepts'?

Back

X-intercepts can also be referred to as zeros, roots, or points where the function crosses the x-axis.

Front

What are the solutions to the equation x^2 - 6x + 8 = 0?

Back

The solutions are x = 2 and x = 4, which can be found by factoring the quadratic.

Front

Which value is a zero of the function f(x) = x^2 + 2x - 3?

Back

The zero of the function is x = -1, as it satisfies the equation f(-1) = 0.

Front

What is the significance of the x-intercepts in a graph?

Back

The x-intercepts indicate the points where the graph of the function crosses the x-axis, representing the values of x for which the function equals zero.

Front

How can you verify if a value is a zero of a function?

Back

To verify if a value is a zero, substitute it into the function. If the result is zero, then it is a zero of the function.

Front

What is the relationship between the factors of a quadratic and its zeros?

Back

The zeros of a quadratic function correspond to the values of x that make each factor equal to zero.

Front

What does the term 'factored form' refer to in quadratic equations?

Back

Factored form refers to expressing a quadratic equation as a product of its linear factors, such as (x - p)(x - q) = 0.

Front

How do you find the x-intercepts of a quadratic function given in standard form?

Back

To find the x-intercepts of a quadratic in standard form, set the equation equal to zero and solve for x using factoring, completing the square, or the quadratic formula.