completing the square
Maths and statistics discussion, revision, exam and homework help.
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Re: completing the squareyes please(Original post by LoveLifeHate)
presuming you want help with this ?? -
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Re: completing the squarex^2 + 2x + 5 = (x + 1)^2 + 4
y = (x + 1)^2 + 4
dy/dx = 2x + 2
at turning point, 0 = 2x + 2
x=-1
at x=-1, y=4
Because of the shape of the graph, the turning point is always a minimum point, so the lowest point is greater than 0. -
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Re: completing the squareAdditionally you can expand it out in your head to make sure it matches the original.(Original post by WarriorInAWig)
I always remember HALF, SQUARE, COPY, DONE when completing the square.
for x^2+bx+c, half b, square b so that you have (x+b/2)^2 - b^2 +c. You should have been told how to interpret a curve in this form. -
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Re: completing the squaresorry but how is the minimum point greater than o when x=-1?(Original post by A.J10)
x^2 + 2x + 5 = (x + 1)^2 + 4
y = (x + 1)^2 + 4
dy/dx = 2x + 2
at turning point, 0 = 2x + 2
x=-1
at x=-1, y=4
Because of the shape of the graph, the turning point is always a minimum point, so the lowest point is greater than 0.
also, q1 the equation is y = x2 + 10x + 19.Last edited by non; 01-07-2012 at 22:34. -
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Re: completing the squareWhen x=-1, f(x)=4. Since (-1, 4) is the minimum/vertex, there does not exist a point on the curve that has a y-coordinate less than 4. Thus, f(x)≥4, and by extension f(x)=x^2+2x+5>0.(Original post by non)
sorry but how is the minimum point greater than o when x=-1?
At a glance, I have no clue how question 2 follows from question 1... -
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Re: completing the squareYou could have stopped at the first line.(Original post by A.J10)
x^2 + 2x + 5 = (x + 1)^2 + 4
y = (x + 1)^2 + 4
dy/dx = 2x + 2
at turning point, 0 = 2x + 2
x=-1
at x=-1, y=4
Because of the shape of the graph, the turning point is always a minimum point, so the lowest point is greater than 0.
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Re: completing the squareGiven the function(Original post by non)
1. Write down the equation of the line of symmetry of the curve y = x2 + 10x + 19.
,
completing the square on the RHS tells us that
Spoiler:Show
Essentially, you have placed the quadratic into vertex form.
It follows that the x-coordinate of the parabola y=ax+by+c's vertex is always
.
You should know that the line of symmetry for a parabola is a vertical line (vertical lines have the equation x=?) and that it crosses the vertex (so we know one x value of the equation x=?).
As such, the equation for said vertical line can be reasoned out. -
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Re: completing the square1.(Original post by non)
1. Write down the equation of the line of symmetry of the curve y = x2 + 10x + 19.
2. Hence show that x2 + 2x + 5 is always positive.
is a quadratic so symmetry occurs at its unique turning point.
Therefore turning point at
is the line of symmetry of .
