.Graph each quadratic relation and determine
i) the y-intercept
ii) the zeros
iii) the equation of the axis of symmetry
iv) the coordinates of the vertex
y = x/2 - 4x - 21
To graph the quadratic relation y = x/2 - 4x - 21, we can start by determining the y-intercept, zeros, axis of symmetry, and vertex.
i) To find the y-intercept, we set x = 0 and solve for y:
y = (0)/2 - 4(0) - 21
y = -21
So the y-intercept is (0, -21).
ii) To find the zeros, we set y = 0 and solve for x:
0 = x/2 - 4x - 21
We can multiply by 2 to eliminate the fraction:
0 = x - 8x - 42
Combining like terms:
0 = -7x - 42
Add 42 to both sides:
7x = -42
Divide both sides by 7:
x = -6
So the quadratic has a single zero at x = -6.
iii) The equation of the axis of symmetry can be found by taking the average of the zeros. Since we only have one zero, the axis of symmetry will be x = -6.
iv) To find the coordinates of the vertex, we can substitute the x-coordinate of the vertex into the equation and evaluate for y:
y = (-6)/2 - 4(-6) - 21
y = -3 + 24 - 21
y = 0
So the vertex is at (-6, 0).
Now we can plot the points and draw the graph.
Here is the graph of the quadratic relation y = x/2 - 4x - 21:
(The graph represents a downward-opening parabola)
y
|
|
|
-21 |
|
|
-6-------+-------+
| x
-6
The y-intercept is -21, the zero is -6, the equation of the axis of symmetry is x = -6, and the vertex is (-6, 0).