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Question 983056: Please help me with this equation.
Express Each equation of no. 1 to 3 in the form a(x+b)^2+c
Sketch the graph of y against x.for each graph,give the coordinates of the points where it intercepts the axes (if any),the gradient of the graph where it cuts the y-axis,the coordinates of the maximum or minimum turning point.draw also its axis of symmetry and write down the equation of the axis.
1. y=3-15x-3x^2
2. y=16-x-x^2
3. y=-x^2-4x-7
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Please help me with this equation.
Express Each equation of no. 1 to 3 in the form a(x+b)^2+c
Sketch the graph of y against x.
For each graph:
a) give the coordinates of the points where it intercepts the axes (if any),
b) the gradient of the graph where it cuts the y-axis,
c) the coordinates of the maximum or minimum turning point.
d) draw also its axis of symmetry and write down the equation of the axis.
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I'll do the 1st one::
1. y = 3-15x-3x^2
y = -3(x^2+5x-1)
Complete the square on x^2 + 5x + 1
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y = -3[x^2+5x+(5/2)^2]+3+3(25/4)
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y = -3(x+(5/2))^2 + (89/4)
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a) give the coordinates of the points where it intercepts the axes (if any),
Ans: y-intercept (0,3)
x-intercepts::
Solve 3x^2 + 15x -3 = 0 using the quadratic formuls
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b) the gradient of the graph where it cuts the y-axis,
Ans:
y' = -6x-15
y'(0) = -15
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c) the coordinates of the maximum or minimum turning point.
Solve::
-6x-15 = 0
x = -5/2
y = f(-5/2) 89/4
d) draw also its axis of symmetry and write down the equation of the axis.
Ans:
axis:: x = -5/2
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Cheers,
Stan H.
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