graph y=-x2-8x-17
In google type:
functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs/
When page be open in blue recatacangle type:
-x^2-8x-17
In Display properties set:
Range x-axis from -8 to 2
Range y-axis from -8 to 2
Then click option Draw
You will see graph of your function.
Your function have y-intercept
y= -17
For x=0
y= -x^2-8x-17= -0^2-8*0-17=0-0-17= -17
If you want to see graph with y-intercept in Display properties set:
Range x-axis from -8 to 2
Range y-axis from -18 to 2
To graph the equation y = -x^2 - 8x - 17, you can follow these steps:
Step 1: Determine the vertex of the parabola.
The vertex of a parabola in the form y = ax^2 + bx + c can be found using the formula x = -b/2a. In this case, a = -1 and b = -8.
x = -(-8) / (2 * -1)
x = 8 / -2
x = -4
To find the corresponding y-coordinate of the vertex, substitute the x-value back into the equation:
y = -(-4)^2 - 8(-4) - 17
y = -16 + 32 - 17
y = -1
So, the vertex of the parabola is (-4, -1).
Step 2: Find the y-intercept.
To find the y-intercept, substitute x = 0 into the equation. In this case, we have:
y = -(0)^2 - 8(0) - 17
y = -17
Therefore, the y-intercept is at (0, -17).
Step 3: Determine the x-intercepts.
To find the x-intercepts, set y = 0 and solve for x.
0 = -x^2 - 8x - 17
This quadratic equation can be solved by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula here:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = -1, b = -8, and c = -17.
x = (-(-8) ± sqrt((-8)^2 - 4(-1)(-17))) / (2 * -1)
x = (8 ± sqrt(64 - 68)) / -2
x = (8 ± sqrt(-4)) / -2
x = (8 ± 2i) / -2
x = 4 ± i
Since the discriminant is negative, the equation has no real solutions. However, it does have complex solutions. The imaginary unit "i" represents the square root of -1.
Step 4: Plot the points on a graph.
Based on the calculations from the previous steps, you can plot the vertex at (-4, -1), the y-intercept at (0, -17), and the complex x-intercepts at (4 + i) and (4 - i).
Step 5: Draw the parabolic curve.
Using the plotted points, you can sketch a smooth curve through them, following the shape of a downward-opening parabola.
The final graph of y = -x^2 - 8x - 17 will resemble a symmetric "U" shape, concave downwards, with the vertex at (-4, -1). The curve will intersect the y-axis at (0, -17). The x-intercepts will be complex numbers, (4 + i) and (4 - i), which means they do not fall on the real x-axis but in the imaginary plane.