Y=x²+2x-8

To prepare for university exams involving this equation, you can do the following: 1. Understand the general form: The equation you provided is a quadratic equation in the form of y = ax² + bx + c, where a = 1, b = 2, and c = -8. Make sure you understand the general properties and solutions of quadratic equations. 2. Graph the equation: Plot the equation on a coordinate plane to visualize its shape and understand its behavior. This can help you identify the intercepts, vertex, and whether the parabola opens upwards or downwards. 3. Find the vertex: The vertex of a quadratic equation in the form y = ax² + bx + c can be found using the formula x = -b/2a. Find the x-coordinate of the vertex by substituting the values of a and b into the formula. Then substitute this x-coordinate back into the equation to find the y-coordinate. 4. Find the intercepts: To find the x-intercepts (zeros) of the equation, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y. 5. Determine the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. It can be found using the x-coordinate of the vertex. 6. Use factoring or the quadratic formula to solve the equation: If you need to find the exact solutions of the equation, you can use either factoring or the quadratic formula. If you need to factor, look for two numbers whose sum is equal to the coefficient of the x-term (2) and whose product is equal to the constant term (-8). Alternatively, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). 7. Analyze the behavior of the equation: Based on the coefficient of the x²-term, determine whether the parabola opens upwards (a > 0) or downwards (a < 0). Also, determine whether the equation has a maximum or minimum value based on the value of a. 8. Review related concepts: Make sure you are familiar with concepts like finding the discriminant (b² - 4ac) to determine the number and nature of the solutions, understanding the relationship between the vertex and the axis of symmetry, and recognizing different forms of quadratic equations (e.g., vertex form, standard form). By following these steps and reviewing related concepts, you can prepare yourself well for university exams involving this quadratic equation.