Activity 1

The quadratic formula is given by $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ , where a, b, and c are coefficients in the equation $$ax^2 + bx + c = 0$$ .

The solutions are $$x = -8, 4$$ .

The solutions are $$x = -1, -\frac{2}{3}$$ .

The factors are $$(x - 1)(x + 3)$$ and the solutions are $$x = 1, x = -3$$ .

The solutions are $$x = 17, -3$$ .

The solutions are $$x = -\frac{5}{3}, -2$$ .

A quadratic equation is a polynomial equation of degree 2, typically in the form $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and $$a \neq 0$$ .

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

The vertex of the parabola represented by the equation $$y = ax^2 + bx + c$$ is given by the point $$\left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right)$$ .

The axis of symmetry for the quadratic function $$y = ax^2 + bx + c$$ is the vertical line given by $$x = -\frac{b}{2a}$$ .