U4LP2 "Characteristics of Quadrarics"

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + 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 represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, found by evaluating the function at x = 0.

Front

How do you find the x-coordinate of the vertex of a quadratic function?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

What does the term 'positive zero' refer to in the context of quadratic functions?

Back

Positive zero refers to the positive x-intercept(s) of the quadratic function, where the graph intersects the x-axis.

Front

What is the significance of the y-value at the vertex?

Back

The y-value at the vertex indicates the maximum or minimum height of the quadratic function, depending on the direction the parabola opens.

Front

How can you determine how long an object will be in the air using a quadratic function?

Back

You can determine how long an object will be in the air by finding the positive zero of the quadratic function that models its height over time.

Front

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

Back

Having two real roots means the graph of the quadratic function intersects the x-axis at two distinct points.

Front

What is the relationship between the coefficients of a quadratic function and its graph?

Back

The coefficients a, b, and c affect the shape, direction, and position of the parabola on the graph.