Identifying Zeros using Graphs and Functions

Front

What are the zeros of a function?

Back

The zeros of a function are the values of x for which the function f(x) = 0. They are also known as x-intercepts.

Front

How can you find the zeros of a quadratic function graphically?

Back

You can find the zeros of a quadratic function by graphing the function and identifying the points where the graph intersects the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It is also the point where the function changes direction.

Front

What is the relationship between the zeros and the factors of a polynomial?

Back

The zeros of a polynomial correspond to the values of x that make each factor equal to zero. If a polynomial can be factored, the zeros can be found by setting each factor to zero.

Front

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

Back

The number of zeros can be determined using the discriminant (D = b^2 - 4ac). If D > 0, there are 2 distinct zeros; if D = 0, there is 1 zero; if D < 0, there are no real zeros.

Front

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

Back

The x-intercepts of a graph represent the points where the function equals zero, indicating the solutions to the equation f(x) = 0.

Front

How can you verify the zeros found graphically?

Back

You can verify the zeros found graphically by substituting them back into the original function to check if they yield a value of zero.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically written in the form ax^2 + bx + c = 0.

Front

What is the role of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.