Question

1. Solve 5x2 = –45x. (1 point)

2. Solve x2 = 14x – 49. (1 point)

3. Solve x2 + 18 = –9x. (1 point)

4. Solve 4x2 = 12x + 40. (1 point)

5. In the following equation, identify the x-intercepts in the graph y = 3x2 + 19x – 40. (2 points)

6. Provide a unique real world example where quadratic equations might be used. (2 points)

Answer 1

1.
\[5x ^{2}=-45x \rightarrow 5x ^{2}+45x=0\rightarrow x ^{2}+9x=0\rightarrow x(x+9)=0\]\[x=0, or,x+9=0\rightarrow x=0,x=-9\]

Answer 2

2.
\[x ^{2}=14x-49\rightarrow x ^{2}-14x+49=0\rightarrow (x-7)^{2}=0\rightarrow x = 7\]

Answer 3

3.
\[x ^{2}+18=-9x \rightarrow x ^{2}+9x+18=0\rightarrow (x+3)(x+6)=0\rightarrow x+3=0,x+6=0\]\[x=-3,x=-6\]

Answer 4

4.
\[4x ^{2}=12x+40\rightarrow x ^{2}=3x+10\rightarrow x ^{2}-3x-10=0\rightarrow (x+2)(x-5)=0\]\[x+2=0,x-5=0\rightarrow x= -2,x=5\]

Answer 5

5.
\[y(x)=3x ^{2}+19x-40\]\[y(x)=0\rightarrow 3x ^{2}+19x-40=0\rightarrow x=(-19\pm \sqrt{19^{2}-4\times3\times(-40)})\div(2\times3)\]\[x=(-19 \pm 29)\div6\rightarrow x=10\div6,x=-8\]

Answer 6

6.
Calculating areas,
ex area of the square \[A(l)=l ^{2}\]
Describing a vertical movement,\[x(t)=x _{0}+v _{0}\times t-g \times t ^{2}\div2\]

Answer 7

Thankss!

Answer 8

Any chance I can get a medal? ;)