Midterm Math 3 (Fall 2024)

The quadratic formula is used to find the solutions of a quadratic equation in the form $$ax^2 + bx + c = 0$$ . It is given by $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

The factored form is $$\left(3x - 2\right)\left(3x - 1\right)$$ .

The solutions are $$x = 4$$ and $$x = -4$$ .

The simplified form is $$1 < x < 5$$ .

The factored form is $$\left(5x + 6\right)\left(x + 1\right)$$ .

The zero product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ .

The standard form is $$y = ax^2 + bx + c$$ , where $$a, b, c$$ are constants and $$a \neq 0$$ .

Factoring a quadratic means expressing it as a product of two binomials, such as $$(px + q)(rx + s)$$ .

The vertex form is $$y = a(x - h)^2 + k$$ , where $$(h, k)$$ is the vertex of the parabola.

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots.