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PtichkaEL [24]
3 years ago
6

Write the equation of the function whose graph is shown. y = (x + )2 +

Mathematics
2 answers:
Deffense [45]3 years ago
8 0
Quadratic form is given in the form
y= ax^{2}+bx+c, where a, b, and c are constants

We substitute the value (8, 12) and (5,3) in turn

12= a(8)^{2}+b(8)+c
12=64a+8b+c ... Equation 1

3=a(5)^{2}+b(5)+c
3=25a+5b+c ... Equation 2

Equation 1 - Equation 2 gives
39a+3b=9, we call this Equation 3

We also know that (5, 3) is the turning point of the curve, where the value of x is given by x=- \frac{b}{2a}
Substitute x=5
5=- \frac{b}{2a}
10a=-b
b=-10a ... Equation 4

Substitute Equation 4 into Equation 3
39a+3b=9
39a+3(-10a)=9
39a-30a=9
9a=9
a=1

Now we need to work out the value of b and c

Substitute a=1 back into equation 4
-10a=b
-10(1)=b
b=-10

Substitute a=1 and b=-10 into either equation 1 or equation 2

64a+8b+c=12
64(1)+8(-10)+c=12
64-80+c=12
c=12+80-64
c=28

Hence the equation of the quadratic curve is
y= x^{2} 10x+28


SCORPION-xisa [38]3 years ago
7 0

Answer:

y=1(x+ -5)² +3

Step-by-step explanation:

1

-5

3

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