Factoring/Solving Quadratics from a graph

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as (x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you find the roots of a quadratic function from its graph?

Back

The roots of a quadratic function can be found by identifying the x-intercepts of the graph, where the function crosses the x-axis.

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 whether it opens upwards or downwards.

Front

What does it mean for a quadratic to be in standard form?

Back

A quadratic is in standard form when it is expressed as ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How can you convert a quadratic from standard form to factored form?

Back

You can convert a quadratic from standard form to factored form by finding the roots using the quadratic formula or factoring directly if possible.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, corresponding to the roots of the 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

How do you determine the direction a parabola opens?

Back

The direction a parabola opens is determined by the sign of the coefficient 'a' in the standard form: if 'a' is positive, it opens upwards; if negative, it opens downwards.

Front

What is the relationship between the roots and the factored form of a quadratic?

Back

The roots of a quadratic equation correspond to the values of x that make the factored form equal to zero.