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So the y-intercept of the parabola is (0,-8). To find the y-intercept we plug in 0 for x: So this parabola has two x-intercepts: (-4,0) and (2,0). To find the x-intercepts we plug in 0 for y: Since "a" is positive we'll have a parabola that opens upward (is U shaped). In this problem: a = 1, b = 2, and c = -8. To find the y-coordinate for the vertex we plug in h in the original equation: To find the x-coordinate for the vertex we use the following formula: So the y-intercept of any parabola is always at (0,c). Notice that if we plug in 0 for x we get: y = a(0) 2 + b(0) + c or y = c. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them. If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the equation factors we can find the points easily, but we may have to use the quadratic formula in some cases. We can find these points by plugging 0 in for y and solving the resulting quadratic equation (0 = ax 2 + bx + c). Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0. If a < 0 (negative) then the parabola opens downward. If a > 0 (positive) then the parabola opens upward. Given y = ax 2 + bx + c, we have to go through the following steps to find the points and shape of any parabola: In order to graph a parabola we need to find its intercepts, vertex, and which way it opens. We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape). The following graphs are two typical parabolas their x-intercepts are marked by red dots, their y-intercepts are marked by a pink dot, and the vertex of each parabola is marked by a green dot: The graph of a quadratic equation in two variables (y = ax 2 + bx + c ) is called a parabola.