Unit 4 Test Algebraic Reasoning

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the term 'zero' of a function refer to?

Back

The 'zero' of a function refers to the value(s) of x for which the function f(x) = 0.

Front

How can you determine the number of real solutions of a quadratic equation?

Back

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

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function intersects the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept of a quadratic function f(x) = ax^2 + bx + c?

Back

To find the y-intercept, substitute x = 0 into the function, resulting in f(0) = c.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula x = -b/(2a) for the x-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, given by the equation x = -b/(2a).

Front

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

Back

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

Front

What does it mean for a quadratic function to have 'no real solutions'?

Back

It means that the graph of the quadratic does not intersect the x-axis at all, indicating that the solutions are complex.

Front

How can you find the solutions of a quadratic equation graphically?

Back

By plotting the quadratic function on a graph and identifying the x-coordinates where the graph intersects the x-axis.