Algebra 2 Exam Review

The height of the rocket (in feet) with respect to time is given by: $$h(t)=-16t^2+vt+h_0$$ , where v is the initial velocity and h_0 is the initial height.

The maximum height occurs at the vertex of the parabola, which can be found using the formula $$t=-\frac{b}{2a}$$ , where a and b are the coefficients from the quadratic equation.

The standard form of a quadratic equation is $$y=ax^2+bx+c$$ , where a, b, and c are constants.

To convert from vertex form $$y=a(x-h)^2+k$$ to standard form, expand the equation: $$y=a(x^2-2hx+h^2)+k$$ .

The coefficient 'a' determines the direction of the parabola (upward if a>0, downward if a<0) and the width of the graph (narrower if |a|>1, wider if |a|<1).

The roots of a quadratic equation are the values of x that make the equation equal to zero, found using the quadratic formula: $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ .

The discriminant is given by $$D=b^2-4ac$$ . It indicates 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.

To simplify square roots, factor the number under the square root into its prime factors and look for pairs. For example, $$\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}$$ .

The vertex of a parabola given in standard form $$y=ax^2+bx+c$$ can be found using the formula $$x=-\frac{b}{2a}$$ and then substituting back to find y.

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