CLASSWORK: Graphing Quadratics in Factored Form

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 can be found by factoring the quadratic equation or using the quadratic formula.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It can be found using the formula x = -b/(2a) for a quadratic in standard form.

Front

How do you find the x-coordinate of the vertex from factored form?

Back

Front

What does it mean if a quadratic has no real solutions?

Back

If a quadratic has no real solutions, it means the parabola does not intersect the x-axis. This occurs when the discriminant (b^2 - 4ac) is less than zero.

Front

How can you determine the number of zeros a parabola has?

Back

The number of zeros can be determined by the discriminant of the quadratic equation. If the discriminant is positive, there are 2 zeros; if it is zero, there is 1 zero; if negative, there are no real zeros.

Front

What is the standard form of a quadratic function?

Back

Front

What is the factored form of a quadratic function?

Back

Front

How do you convert from factored form to standard form?

Back

To convert from factored form to standard form, expand the expression by multiplying the factors and combining like terms.

Front

What is the axis of symmetry of a parabola?

Back

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient (a) determines the direction of the parabola. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.