How do you use the important points to sketch the graph of #y=x^2+4x+6#?
Put in zero, 1, -1, 2, -2 for x
Putting in x for zero give the value for y where the curve begins. y = 6
then putting in the small values for x fives a points to start the sketch of the graph
When x = 1 y = 11 When x = -1 y = 3
When x = 2 y = 18 When x = -2 y = 2
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The important points which you need for sketching a curve are:
- the
#y# -intercept - the
#x# -intercept(s) - the vertex (turning point)
Completing the square gives:
graph{y =x^2+4x+6 [-6.997, 3.003, 1.76, 6.76]}
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To sketch the graph of ( y = x^2 + 4x + 6 ), follow these steps:
-
Identify the vertex: The vertex of the parabola represented by the equation ( y = ax^2 + bx + c ) is given by the coordinates ((h, k)), where ( h = -\frac{b}{2a} ) and ( k = f(h) ).
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Calculate the vertex: Substitute ( h = -\frac{b}{2a} ) into the equation to find the y-coordinate of the vertex.
-
Find the y-intercept: Set ( x = 0 ) and solve for ( y ).
-
Find the x-intercepts (if any): Set ( y = 0 ) and solve the quadratic equation for ( x ).
-
Plot the vertex, y-intercept, and x-intercepts on the coordinate plane.
-
Determine the direction of the parabola: If ( a > 0 ), the parabola opens upwards. If ( a < 0 ), the parabola opens downwards.
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Sketch the graph: Use the important points and the direction of the parabola to sketch the graph smoothly through those points.
Remember to label the axis and any significant points on the graph.
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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.
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.
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.
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.
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