Answer:
Step-by-step explanation:
We can answer this in two ways: Differentiation and Graphing.
<u>Differentitate:</u>
The first derivative of a function yields a function that provides the slope for any point on the line of the original function. The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.
f(x) = 3(x-1)^2 + 4
f(x) = 3(x-1)(x-1) + 4
f(x) = 3(x^2 - 2x + 1) + 4
f(x) = 3x^2 - 6x + 7
f'(x) = 6x -6
Set this = 0 and find x:
0 = 6x -6
x = 1
The value of y when x=1 in the original equation is:
f(1) = 3(1-1)^2 + 4
y = 4
The vertex is (1,4)
<u>Graph:</u>
You can use DESMOS to plot the function. The result is attached. Look for the vertex and read the coordinates. (1,4) seems to work.
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant.
Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:
<u>Your y-intercept is (0,-51).</u>
Next, using our equation plug the appropriate values into the quadratic formula:
Next, solve the multiplications and exponent:
Next, solve the addition:
Now, simplify the radical using the product rule of radicals as such:
- Product Rule of Radicals: √ab = √a × √b
√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34
Next, divide:
<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>
Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:
<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>
The answer is 13, i got this by using the pythagorean theorem. a^2 + b^2 = c^2. in this case it would be 84^2 + b^2 = 85^2. then that would turn into 7056 + b^2 = 7225, subtract both sides by 7056 to get b^2 = 169, then square 169 to get 13 :)
Which question to answer?
Answer:
yes
Step-by-step explanation:
the second number in a set of parenthesis is the y value and the number in the parenthesis is 92 which makes y=92 true
