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`A^('')`

аあ Ask Copilot Solve the equations graphically by sketching the graphs of the corresponding functions. a)

`|4x+2|=3x+5`

(4 marks) b)

`2x-8=|x^(2)-2x-8|`

(5 marks) Solve the equations graphically using a graphing utility. a)

`3-5x=|4x-6|`

(3 marks) b)

`|x^(2)-x|=2x^(2)+x-3`

(3 marks) Solve these equations algebraically. a)

`|5x-8|=2`

(2 marks) b)

`2-2x=|4-x|`

(3 marks) c)

`|3x-5|=x-1`

(3 marks) d)

`|(1)/(2)x-3|=-5`

(2 marks) e)

`|x^(2)-8x+12|=21`

(5 marks) f)

`|x^(2)-4|=4-x`

(4 marks) g)

`|3+x-2x^(2)|=5-x`

(6 marks) You're trying to solve the equation

`|x^(2)-5x-8|=-2`

. Your classmate tells you that there's no solution. Are they right or wrong? Justify your answer. (3 marks) a) Find the vertex of

`y=x^(2)-3x-10`

. (3 marks) b) Explain how the

`y`

-value at the vertex can show you if the equation

`|x^(2)-3x-10|=30`

will have 2 or 4 solutions. (3 marks)