Hi:) why is the gradient of vertical lines undefined?
1 answer:
Answer:
The gradient of a line is given by .
Any 2 points of a vertical line would have the same x-coordinate. Thus when you simplify the denominator, you would end up with a zero. If you enter that into your calculator, no matter what you numerator is, you would get a Math error. This is because you cannot possibly divide a number by zero. Thus, the gradient is undefined.
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Answer:
Step-by-step explanation:
The standard form of a quadratic equation is
The vertex form of a quadratic equation is
The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.
To find the h-value of the vertex, you use the following equation:
In this case, our quadratic equation is . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.
⇒
Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is
⇒
⇒
⇒
This y-value that we just found is our k-value.
Next, we are going to set up our equation in vertex form. As a reminder, vertex form is:
a: 1
h: 3
k: -25
Hope this helps!