Answer:
y = - (x - 5)² + 7
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (5, 7 ) , then
y = a(x - 5)² + 7
To find a substitute (10, - 3 ) into the equation
- 3 = a(10 - 5)² + 7 ( subtract 7 from both sides )
- 10 = 5²a = 25a ( divide both sides by 25 )
= a , that is
a = -
y = - (x - 5)² + 7 ← in vertex form
Answer:
Option B. minimum is correct for the first blank
Option C. 6 is correct for second blank.
Step-by-step explanation:
In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.
Given function is:
Taking first derivative
Now the first derivative has to be put equal to zero to find the critical value
The function has only one critical value which is 5.
Taking 2nd derivative
As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5
The value can be found out by putting x=5 in the function
Hence,
<u>The function y = x 2 - 10x + 31 has a minimum value of 6</u>
Hence,
Option B. minimum is correct for the first blank
Option C. 6 is correct for second blank.