Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y=-x^2-2x
find the x-intercepts. y=x^2+4x
looks like you are asking 2 separate questions
for the first :
why not pick integer values of x from -4 to +4 then plot those points.
That should give you a good idea what kind of parabola you have.
That should also give you a good idea where the vertex is.
Remember the axis of symmetry goes through the vertex.
for the second :
doesn't y = x^2 + 4x factor to
y = x(x+4) ?
Can you see what values of x would make the y equal to zero?
-4 is the answer? i think because i an only 10 and in year 6
To identify the axis of symmetry and graph the equation, let's follow these steps:
Step 1: Find the axis of symmetry.
The equation is in the form y = ax^2 + bx + c, where a = -1, b = -2, and c = 0.
The axis of symmetry can be found using the formula x = -b/(2a).
Substituting the values, we have x = -(-2)/(2*(-1)) = -(-2)/(-2) = 1.
Therefore, the axis of symmetry is x = 1.
Step 2: Create a suitable table of values.
To sketch the graph, let's choose some x values and calculate the corresponding y values.
Let's select x values: -2, -1, 0, 1, 2.
Using these x values, we can calculate the corresponding y values:
For x = -2:
y = -(-2)^2 - 2(-2) = -4 + 4 = 0.
For x = -1:
y = -(-1)^2 - 2(-1) = -1 + 2 = 1.
For x = 0:
y = -(0)^2 - 2(0) = 0.
For x = 1:
y = -(1)^2 - 2(1) = -1 - 2 = -3.
For x = 2:
y = -(2)^2 - 2(2) = -4 - 4 = -8.
Step 3: Sketch the graph.
Now that we have the table of values, we can plot the points on the graph and draw the curve.
The axis of symmetry is x = 1, which means the graph will be symmetric with respect to this line.
The graph should look like a downward-opening parabola with maximum point (1, -3). Make sure to label the points we calculated on the table.
Here is the graph:
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_____+_____\______
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(1,-3)
Note: The axis of symmetry is a vertical line passing through the vertex of the parabola and divides it into two equal halves.