Answer:
Explanation:
Let’s assume the quadratic function has
the form: f(x) = ax? + bx + c.
We can substitute the given points into the function to form a system of equations.
Substituting (0,5) into the function
gives us: 5 = a(0)2 + 6(0) + c, which
simplifies to c = 5.
Substituting (2, 13) into the function
gives us: 13 = a(2)? + 6(2) + 5, which
simplifies to 4a + 26 = 8.
Substituting (3, 26) into the function
gives us: 26 = a(3) + 6(3) + 5, which
simplifies to 9a + 36 = 18.
We now have a system of equations:
C=5
4a + 26 = 8
9a + 36 = 18
We can solve this system of equations using any method. Let’s use the
substitution method.
From the first equation, we know that
c = 5. We can substitute this value into
the other two equations.
Substituting c = 5 into the second
equation gives us: 4a + 26 = 8.
Substituting c = 5 into the third
equation gives us: 9a + 36 = 18.
Solving the system of equations:
From Step 6, we can simplity the
equation to: 2a + b = 4.
From Step 7, we can simplify the
equation to: 3a + b = 6.
Subtracting the first equation from the second equation eliminates the
variable b: (3a + b) - (2a + 6) = 6 - 4,
which simplifies to a = 2.
Substituting a = 2 into the first
equation gives us: 2(2) + b = 4, which
simplifies to 4 + b = 4, and further
simplifies to b = 0.