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The following is a selected video from your teacher comm where you can browse over 450 complete math lessons with example videos interactive practice problems self tests and more try a complete lesson today at your teacher calm here we're asked to graph the parabola Y minus 2 equals negative 1/7 times parentheses X plus 7 squared using its vertex and intercepts and write the equation of its axis of symmetry remember that our formula for a parabola is y minus K equals a times parentheses X minus H squared and notice that H equals negative 7 and K equals 2 which means that the vertex of the parabola HK is negative 7/2 so let's start by plotting this point on the graph next to find the y-intercept of the parabola we're looking for the point where it crosses the y-axis and notice that any point on the y-axis has an x-coordinate of 0 so to find the y intercept we plug a 0 into our equation for X, and we have Y minus 2 equals negative 1/7 times parenthesis 0 plus 7 squared simplifying on the right side we have Y minus 2 equals negative 1/7 times 7 squared or Y minus 2 equals negative 1/7 times 49 negative 1/7 times 49 is negative 7, so we have Y minus 2 equals negative 7 and adding 2 to both sides y equals negative 5 so the y intercept of the parabola is negative 5 which is the point five units down on the y-axis next to find the x intercepts of the parabola or the points where the parabola crosses the x-axis remember that we plug a zero into our equation for y, and we have zero minus two equals negative 1/7 times parentheses X plus seven squared simplifying on the left side we have negative 2 equals negative 1/7 times parentheses x plus 7 squared now to get X by itself we first get rid of the fraction on the right side of the equation by multiplying both sides by 7 that gives us negative 14 equals negative 1 times X plus 7 squared next we divide both sides by negative 1, and we have 14 equals x plus 7 squared since the squared term is now by itself we can take the square root of both sides of the equation, and we have plus or minus root 14 equals x plus 7 remember to always use plus or minus when square rooting both sides of an equation using our calculator we find that the square root of 14 is approximately equal to 3 point 7, so we have plus or minus 3.7 equals x plus 7 now to get X by itself we subtract 7 from both sides, and we have negative 7 plus or minus 3.7 equals x which means that negative 7 plus 3 point 7 equals x or negative 7 minus 3 point 7 equals x negative 7 plus 3 point 7 is negative 3 point 3 so negative 3 point 3 equals x and negative 7 minus 3 point 7 equals negative 10 point 7 so negative 10 point 7 equals x so the x-intercepts or the points where the parabola crosses the x-axis our negative 3 point 3 and negative 10 point 7 now we draw our parabola by connecting the vertex and the intercepts remember that a parabola is symmetrical, so we can approximate its shape based on our given points finally remember that the axis of...