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

A quadratic is in factored form when it is expressed as $$a(x - p)(x - q)$$ , where p and q are the roots of the equation.

What is the discriminant and how is it used?

The discriminant is given by $$D = b^2 - 4ac$$ . It determines the nature of the roots: if D > 0, there are two real roots; if D = 0, one real root; if D

How do you determine if a quadratic opens upwards or downwards?

A quadratic opens upwards if the coefficient $$a > 0$$ and downwards if $$a

What is the significance of the vertex in a quadratic function?

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.

How do you find the axis of symmetry for a quadratic function?

The axis of symmetry can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the relationship between the roots and the coefficients of a quadratic equation?

The sum of the roots is given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

What is the process of completing the square?

Completing the square involves rewriting a quadratic in the form $$x^2 + bx$$ as $$(x + \frac{b}{2})^2 - \frac{b^2}{4}$$ .

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and plot additional points to shape the parabola.

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What is the quadratic formula used to find the solutions of a quadratic equation?

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