Finding Zeros

The standard form of a quadratic equation is $$y=ax^2+bx+c$$ .

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

To find the zeros of a quadratic function, set the equation equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

The zeros of the function are $$-6$$ and $$4$$ .

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

The vertex can be found using the formula $$x=-\frac{b}{2a}$$ , where $$a$$ and $$b$$ are coefficients from the standard form.

The roots of the equation are $$-3$$ and $$2$$ .

The quadratic formula is $$x=\frac{-b\text{±}\text{√}(b^2-4ac)}{2a}$$ , used to find the roots of a quadratic equation.

A zero of a function is a value of x that makes the function equal to zero.

You can determine if a quadratic function has real roots by checking the discriminant $$b^2-4ac$$ . If it is positive, there are two real roots; if zero, one real root; if negative, no real roots.