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Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²-2x=35. If there is more than one x-intercept, separate them with commas. Please help?

Answer 1

Christian Antunez

#(1,-36),x=-5,x=7#

#"express the equation in standard form";ax^2+bx+c#

#y=x^2-2x-35#

#"the factors of - 35 which sum to - 2 are - 7 and + 5"#

#(x-7)(x+5)=0larrcolor(blue)"for intercepts"#

#rArrx=-5,x=7larrcolor(red)"x-intercepts"#

#"the vertex lies on the axis of symmetry which is"# #"situated at the midpoint of the intercepts"#

#x_(color(red)"vertex")=(7-5)/2=1#

#"substitute x into equation for y"#

#y_(color(red)"vertex")=1-2-35=-36#

#color(magenta)"vertex "=(1,-36)#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.