Comments and Help with graphing quadratic equations worksheet answers

Video instructions and help with filling out and completing worksheet graphing quadratics from standard form

Instructions and Help about graphing quadratic functions in standard form worksheet answer key

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 symmetry is...