X=x^2+3x-10. Graphed as a parabola
Include the x,y table please.
And line of symmetry.
In google type:
functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs/
When page be open in blue rectangle type:
x^2+3x-10
Set:
Range x-axis from -6 to 4
Range y-axis from -13 to 7
and click option:
Draw
The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis.
The formula for the line of symmetry:
h = – b / 2 a
In this case :
a = 1
b = 3
h = –b / 2 a
h = - 3 / 2 * 1 =
h = - 3 / 2
x , y table:
x = - 3 , y = - 10
x = - 2 , y = - 12
x = - 1 , y = - 12
x = 0 , y = - 10
x = 1 , y = -6
x = 2 , y = 0
x = 3 , y = 8
etc.
To graph the parabola represented by the equation X = x^2 + 3x - 10, we can start by creating an x-y table to find some key points.
We can choose a range of x values and substitute them into the equation to determine the corresponding y values. Let's use x values from -5 to 5:
x | y
---------
-5 |
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
To find the y values, we substitute each x value into the equation:
For x = -5:
X = (-5)^2 + 3(-5) - 10
X = 25 - 15 - 10
X = 0
So, when x = -5, y = 0.
You can now fill in the y values for each corresponding x value in the table.
x | y
---------
-5 | 0
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
Now, to find the line of symmetry, we can make use of the vertex formula. The vertex form of a parabola is given by x = -b/2a, where a and b are the coefficients of the quadratic equation.
In this case, the equation X = x^2 + 3x - 10 is in standard form, so we can identify a = 1 and b = 3.
x = -3/2(1) = -3/2 = -1.5.
The line of symmetry is represented by the equation x = -1.5.
Now, let's plot the points on a graph and draw the parabola.
Once we have the graph, we can locate the line of symmetry.
To graph the equation X = x^2 + 3x - 10 as a parabola, we can start by finding the vertex and the line of symmetry.
The equation of the parabola is in the form of y = ax^2 + bx + c, where a, b, and c are constants. In this case, we have x as the dependent variable rather than y, so we can rewrite the equation as:
y = x^2 + 3x - 10
To find the vertex, we can use the formula x = -b/2a. In our equation, a = 1 and b = 3. Plug these values into the formula:
x = -3/(2*1)
x = -3/2
x = -1.5
To find the y-coordinate of the vertex, substitute the value of x back into the equation:
y = (-1.5)^2 + 3*(-1.5) - 10
y = 2.25 - 4.5 - 10
y = -12.25
So the vertex of the parabola is (-1.5, -12.25).
To find the line of symmetry, the formula is x = -b/2a. Again, substitute the values of a and b into the formula:
x = -3/(2*1)
x = -3/2
x = -1.5
So the line of symmetry is x = -1.5.
To generate an x, y table, we can pick some x-values and substitute them into the equation to find their corresponding y-values. Let's choose x-values of -3, -2, -1, 0, 1, and 2:
When x = -3:
y = (-3)^2 + 3*(-3) - 10
y = 9 - 9 - 10
y = -10
When x = -2:
y = (-2)^2 + 3*(-2) - 10
y = 4 - 6 - 10
y = -12
When x = -1:
y = (-1)^2 + 3*(-1) - 10
y = 1 - 3 - 10
y = -12
When x = 0:
y = (0)^2 + 3*(0) - 10
y = 0 - 0 - 10
y = -10
When x = 1:
y = (1)^2 + 3*(1) - 10
y = 1 + 3 - 10
y = -6
When x = 2:
y = (2)^2 + 3*(2) - 10
y = 4 + 6 - 10
y = 0
The x, y table for these values is as follows:
| x | y |
| -3 | -10 |
| -2 | -12 |
| -1 | -12 |
| 0 | -10 |
| 1 | -6 |
| 2 | 0 |
Now, we can plot these points on a graph and draw a smooth curve passing through them. The line of symmetry is a vertical line passing through the vertex (-1.5, -12.25).