Y=x²+2x-8
To prepare for university exams, I suggest reviewing the properties and equations of quadratic functions. Let's start by analyzing the equation y = x² + 2x - 8.
Vertex: The vertex of a quadratic function y = ax² + bx + c can be found using the formula x = -b/2a. In this case, a = 1, b = 2, and c = -8. Plugging these values into the formula, we get x = -2/(2*1) = -1. The y-coordinate of the vertex can be found by substituting this value of x back into the equation: y = (-1)² + 2(-1) - 8 = -7. Therefore, the vertex of the parabola is (-1, -7).
Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. The equation of this line can be written as x = -b/2a. So, in our case, the axis of symmetry is x = -2/(2*1) = -1.
Intercepts: To find the x-intercepts, set y = 0 and solve for x. In this case, we have x² + 2x - 8 = 0. This equation can be factored as (x + 4)(x - 2) = 0, which gives us two solutions: x = -4 and x = 2. Therefore, the x-intercepts are (-4, 0) and (2, 0).
To find the y-intercept, substitute x = 0 into the equation: y = (0)² + 2(0) - 8 = -8. So, the y-intercept is (0, -8).
Graph: Plot the vertex (-1, -7), the x-intercepts (-4, 0) and (2, 0), and the y-intercept (0, -8) on a graph. Connect the points to create a smooth parabolic curve.
Remember to also study other concepts related to quadratic functions, such as finding the maximum or minimum value, using the quadratic formula, and solving word problems involving quadratics. Good luck with your exams!
