5.7&5.8 HW Determine Quadratic Function and Systems

Front

What are the zeroes of a quadratic function?

Back

The zeroes of a quadratic function are the values of x for which the function equals zero. They can be found by factoring, using the quadratic formula, or completing the square.

Front

How do you determine the quadratic function from its zeroes?

Back

If a quadratic function has zeroes at x = a and x = b, it can be expressed as f(x) = k(x - a)(x - b), where k is a non-zero constant.

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 it mean for a quadratic function to have one root?

Back

A quadratic function has one root (or a repeated root) when its discriminant (b^2 - 4ac) is equal to zero, indicating that the parabola touches the x-axis at one point.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form ax^2 + bx + c = 0, factor it into the form (px + q)(rx + s) = 0, and then set each factor to zero.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point (x, y) is a solution, substitute the x-value into both equations and check if the resulting y-values are equal to the y-value of the point.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form f(x) = ax^2 + bx + c is given by the coordinates (h, k), where h = -b/(2a) and k = f(h).

Front

What is the discriminant of a quadratic equation?

Back

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. It determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means two complex roots.

Front

What is a system of non-linear equations?

Back

A system of non-linear equations consists of two or more equations where at least one of the equations is not linear, meaning it includes variables raised to a power greater than one.