Period+1+Group+1

Graph: F



The graph is a parabola which means this is a quadratic function which can be written in the form y= ax^2+bx+c. We know the a value is negative, because if the a is negative, the vertex is a maximum and the graph opens downwards. This matches our graph, so our a value is negative. To find the actual a value, you would use a(x-m)(x-n) where M and N are the x-intercepts which are (-2,0) and (2,0) as shown on the graph how is this shown on the graph? . So now we have y = a(x+2)(x-2). To solve for a, we take a point on the parabola (-1,3) and plug it in. This gives us 3=a(-1+2)(-1-2) which is 3=a(1)(-3) which is 3=-3a so a= -1

Next I found the b value. I determined the b value was 0 because the graph is centered symmetric over the y axis. The graph only becomes centered when the b value equals 0, so i knew that the b= 0. This means we do not need to include the b value in our final equation, so we will have y= -1 x ^2 + c

To find the c value, we would find the y intercept since the c value equals the y intercept which is (0,4) explain where you see it in the graph so c= 4

Our final equation is y= -1x^2 + 0x + 4 or y= -1x^2 + 4

Graph: I



The graph is a parabola which means this is a quadratic function which can be written in the form y= ax^2+bx+c. We know the a value is negative, because if the a is negative, the vertex is a maximum and the graph opens downwards. This matches our graph, so therefore our a value is negative. To find the actual a value, you would use a(x-m)(x-n) where M and N are the x-intercepts which are (-1,0) and (2,0) as shown on the graph where. So now we have y = a(x+1)(x-2). To solve for a, we take a point on the parabola (0,4) and plug it in. This gives us 4=a(0+1)(0-2) which is 4=a(1)(-2) which is 4=a(-2) so a= -2

To find the b value, I plugged the a value into a(x-m)(x-n) which is -2(x+1)(x-2). This equals -2(x^2-2x+1x-2) when FOILED out. This equals -2(x^2-x-2) which is -2x^2+2x+4. So b=2.

To find the c value, didn't you find the y-intercept above? we would find the y intercept how did you find it? since the c value equals the y intercept which is (0,4) so c= 4

Our final equation is y= -2x^2 +2x +4