Final answer:
The equation presented is a quadratic equation, solvable by substitution, factoring, completing the square, or applying the quadratic formula. It can be graphed by calculating y for various x values or analyzing the parabola's properties.
Step-by-step explanation:
Solving a Quadratic Equation
The equation y = x² + 4x - 2 is indeed a quadratic equation, which is a second-degree polynomial equation in a single variable x. Quadratic equations have the form ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0. To find the value of y for a given x-value, we simply substitute the value into the equation and solve for y. For example, if x = 2, then y = (2)² + 4(2) - 2.
To graph this equation or find its roots, we could use various methods such as factoring, completing the square, or using the quadratic formula. Specifically, this equation could be graphed by plotting data pairs after calculating y for a range of x values or by finding the vertex and axis of symmetry for a parabola that this equation represents when graphed on the Cartesian plane.
Understanding how to manipulate and solve these equations is fundamental in algebra and precalculus coursework and appears often in STEM-related fields.