Tell whether the graph opens upward or downward. Then find the axis of symmetry and vertex of the graph of the function.
y=-1/4x^2-24
y=-1/4x^2-24
Hints:
If the leading coefficient of a quadratic expression is negative, it opens downwards.
For a general quadratic equation
y=ax²+bx+c,
The axis of symmetry is at the line
y=-b/2a
Which one is the B in my equation?
y=ax²+bx+c,
b is the coefficient of the term in x.
Since your expression does not have an x-term, b=0.
Thank you!
You're welcome!
To determine whether the graph of the function opens upward or downward, we can observe the coefficient of the x^2 term. The function is in the form of y = ax^2 + bx + c, where a is the coefficient of the x^2 term.
In the given function y = -1/4x^2 - 24, the coefficient of the x^2 term is -1/4. Since a is negative, the graph of the function opens downward.
Now, let's find the axis of symmetry and the vertex of the graph.
The axis of symmetry can be found using the formula x = -b/2a. In this case, b is 0 (since there is no x term), and a is -1/4.
x = -0/2(-1/4) = 0/0 (undefined)
Since the formula gives an undefined result, we can conclude that the graph does not have a vertical axis of symmetry. Instead, it has a vertical line of symmetry at x = 0 (the y-axis).
To find the vertex, we substitute x = 0 into the function and solve for y.
y = -1/4(0)^2 - 24
y = 0 - 24
Therefore, the vertex of the graph is (0, -24).
In summary, the graph of the function y = -1/4x^2 - 24 opens downward, does not have a vertical axis of symmetry, and its vertex is at (0, -24).