# Investigating the Quadratic Function.

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Introduction

Investigating the Quadratic Function

Type 1

Dan Plant

Mr. Maly

11 IB Mathematics

Thursday, May 10, 2007

Investigating the Quadratic Function Type 1

- Based on three resulting graphs, it can be determined that they are in fact all the same shape, of a parabola, however have varied locations. Furthermore, the locations of the graphs are specifically translated positively or negatively vertical according to the constant added or subtracted to the variable (x2). These three graphs may be generalized by the following statement; adding a positive or negative constant h will shift the graph vertically h units in the function y = (x2)+h. (Refer to attached graphs)
- Based on the three resulting graphs, it can be determined that they are in fact all the same shape, of a parabola, however they have varied locations. Furthermore, the locations of the graphs are specifically translated

Middle

(c) (i) x2 – 18x + 77 (ii) x2 – 14x + 57 (iii) x2 + 12x + 36 (iv) x2 –5x + 8.5

(i) x2 – 18x + 77→ x2 – 18x + (81 – 4) → (x2 – 18x + 81) – 4 →(x – 9)2 - 4

(ii) x2 – 14x + 57→ x2 – 14x + (49 + 8) → (x2 – 14x + 49) + 8 →(x – 7)2 + 8

(iii) x2 + 12x + 36→(x + 4)2

(iv) The middle term of the following expression, x2 – 7x + 14.5, determines the constant h of (x – h)2. Therefore, h will equal 7/2. The resultant of (x – h)2, (x - 7/2)2, is x2 – 7x + 12.25. In order to achieve an expression equal to the original, it is required to add 2.25 in the place of the constant g. With the addition of the necessary 2.25, equalizing it to the original expression in the x2

Conclusion

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