is a the slope and c the y intercept? what's b?
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Great question. Unfortunately, it's not quite that simple when you have a parabola in that form. But here's what you CAN tell:
1) The parabola will be U-shaped if a>0, and upside down U if a<0
2) The parabola will be shifted up c units when compared to the parabola ax^2 + bx.
3) The y-intercept of the parabola will be f(0) = a*0 + b*0 + c = c
4) The x-intercepts will be when f(x) = 0. Thus, they will happen at the solutions of the quadratic equation. You may have 2 intercepts if b^2 - 4ac > 0, 1 intercept if b^2 - 4ac = 0, or no intercepts if b^2 - 4ac < 0.
5) The x-coordinate of the vertex is at -b/2a. The y-coordinate of this vertex is found by plugging in x = -b/2a into ax^2 + bx + c.
Those aren't really handy for graphing, however. What you do in practice if you want to graph ax^2 + bx + c is you complete the square. You get it in the form a(x-h)^2 + k. From this, you can read alot of graphical information easily:
1) a is still the same parameter as above, so it's still upside down when a<0, and U-shaped when a>0.
2) If 0 < |a| < 1, then it's a fat parabola. If |a| > 1, it's a skinny parabola.
3) The vertex of the parabola is at (h,k). If you get something like (x+3)^2 + 4, change the (x+3)^2 to (x - -3)^2, and you can see that it has a vertex at (-3, 4).
The first form that you give has handy ways of determing x and y-intercepts - the quadratic formula and simply (0, c), respectively. The second form is handy for determing the "fatness" of the parabola, and also is handy for locating the vertex.
1) The parabola will be U-shaped if a>0, and upside down U if a<0
2) The parabola will be shifted up c units when compared to the parabola ax^2 + bx.
3) The y-intercept of the parabola will be f(0) = a*0 + b*0 + c = c
4) The x-intercepts will be when f(x) = 0. Thus, they will happen at the solutions of the quadratic equation. You may have 2 intercepts if b^2 - 4ac > 0, 1 intercept if b^2 - 4ac = 0, or no intercepts if b^2 - 4ac < 0.
5) The x-coordinate of the vertex is at -b/2a. The y-coordinate of this vertex is found by plugging in x = -b/2a into ax^2 + bx + c.
Those aren't really handy for graphing, however. What you do in practice if you want to graph ax^2 + bx + c is you complete the square. You get it in the form a(x-h)^2 + k. From this, you can read alot of graphical information easily:
1) a is still the same parameter as above, so it's still upside down when a<0, and U-shaped when a>0.
2) If 0 < |a| < 1, then it's a fat parabola. If |a| > 1, it's a skinny parabola.
3) The vertex of the parabola is at (h,k). If you get something like (x+3)^2 + 4, change the (x+3)^2 to (x - -3)^2, and you can see that it has a vertex at (-3, 4).
The first form that you give has handy ways of determing x and y-intercepts - the quadratic formula and simply (0, c), respectively. The second form is handy for determing the "fatness" of the parabola, and also is handy for locating the vertex.