This is the whole problem. The work, the graph and the parent function along with the answers to create the graph.
This is the picture to show the steps and the graph to show you what the function becomes. You begin with your standard function. Then you add two to both sides of the equation. After that you take out the leading coefficient which is in this case -4. Make sure you have that on both sides of your equation to keep in line with the math rule, whatever you do to one side you must do to the other. Then you take your b. -3, and divide it by 2, giving you -3/2. Then you square your answer giving you 9/4. Add 9/4 to both sides within your parenthesis. Now you should have -4(x^2-3x+9/4)=2-4(9/4). After that you reduce your quadratic on the left and solve on the right. You should be left with the answer -4(x-3/2)^2=-7. Once you have that, you add 7 to both sides and get your parent function equation (also known as graphing equation) which is f(x)=-4(x-3/2)^2+7. From here you get your vertex (h,k) and that is (3/2,7) reduced is (1.5,7). Then you get your axis from that, which is the x-value so your x-intercept is 1.5. After that you go back to the equation right before the addition of the seven and find your x-intercepts by solving for x. You divide both sides by -4 then take the square root of both sides and finally add 3/2 to both sides. That makes your x-intercepts, with the 3/2 reduced, (1.5+√7/2,0) and (1.5-√7/2,0). To approximate that plug them both into your calculator and round to the nearest hundredths/thousandths place. Your x-intercepts become (2.82,0) and (.177,0). Then you find your y-intercept and to do that you plug zero into the x in the standard form and you get your answer of (0,-2). [The blue highlights are the parent function, the orange is your non-reduced and reduced x-intercepts, green is your vertex, pink dashes are your axis, and the purple is your y-intercept.] Then you plot each point, draw your dashed axis and connect the dots. Do not forget to reflect your y-intercept across the axis.
This is just the answers put into the key and color coded onto the graph for a nice visual. Your vertex in this equation is a maximum due to the negative a.
This is the whole problem. The work, the graph and the parent function along with the answers to create the graph. 
This is the picture to show the steps and the graph to show you what the function becomes. You begin with your standard function. Then you add two to both sides of the equation. After that you take out the leading coefficient which is in this case -4. Make sure you have that on both sides of your equation to keep in line with the math rule, whatever you do to one side you must do to the other. Then you take your b. -3, and divide it by 2, giving you -3/2. Then you square your answer giving you 9/4. Add 9/4 to both sides within your parenthesis. Now you should have -4(x^2-3x+9/4)=2-4(9/4). After that you reduce your quadratic on the left and solve on the right. You should be left with the answer -4(x-3/2)^2=-7. Once you have that, you add 7 to both sides and get your parent function equation (also known as graphing equation) which is f(x)=-4(x-3/2)^2+7. From here you get your vertex (h,k) and that is (3/2,7) reduced is (1.5,7). Then you get your axis from that, which is the x-value so your x-intercept is 1.5. After that you go back to the equation right before the addition of the seven and find your x-intercepts by solving for x. You divide both sides by -4 then take the square root of both sides and finally add 3/2 to both sides. That makes your x-intercepts, with the 3/2 reduced, (1.5+√7/2,0) and (1.5-√7/2,0). To approximate that plug them both into your calculator and round to the nearest hundredths/thousandths place. Your x-intercepts become (2.82,0) and (.177,0). Then you find your y-intercept and to do that you plug zero into the x in the standard form and you get your answer of (0,-2). [The blue highlights are the parent function, the orange is your non-reduced and reduced x-intercepts, green is your vertex, pink dashes are your axis, and the purple is your y-intercept.] Then you plot each point, draw your dashed axis and connect the dots. Do not forget to reflect your y-intercept across the axis.
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