Quadratic Characteristics Math I Flashcard Review

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They are also known as the x-intercepts of the graph.

Front

What does the leading coefficient of a quadratic function indicate about its graph?

Back

The sign of the leading coefficient indicates the direction of the parabola. If the leading coefficient is positive, the parabola opens upwards; if it is negative, it opens downwards.

Front

What is another term for the x-intercept of a function?

Back

Zeros.

Front

What is the definition of an x-intercept?

Back

An x-intercept is a point on the graph of a function where the value of y is zero.

Front

What is the definition of a y-intercept?

Back

A y-intercept is a point on the graph of a function where the value of x is zero.

Front

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

Back

You can find the zeros of a quadratic function by setting the function equal to zero and solving for x, often using factoring, the quadratic formula, or completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the zeros of a quadratic equation ax² + bx + c = 0.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction the parabola opens.

Front

How do you determine the vertex of a quadratic function in standard form?

Back

For a quadratic function in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex. Its equation is x = -b/(2a).