Select all the expressions that are equivalent to 25 + 3(a - 5) + 7a (A) 10a + 20 D 10a + 10 B 8a + 23 E 2(5a + 10) 5(2a + 2)
1 answer:
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Answer:
The inverse of f(x) is (x) = ±
+
Step-by-step explanation:
To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where
- h =
- k is the vlue f at x = h
∵ f(x) = 3x² - 3x - 2
→ Compare it with the 1st form above to find a and b
∴ a = 3 and b = -3
→ Use the rule of h to find it
∵ h = =
=
∴ h =
→ Substitute x by the value of h in f to find k
∵ k = 3( )² - 3(
) - 2
∴ k =
→ Substitute the values of a, h, and k in the vertex form above
∵ f(x) = 3(x - )² +
∴ f(x) = 3(x - )² -
Now let us find the inverse of f(x)
∵ f(x) = y
∴ y = 3(x - )² -
→ Switch x and y
∵ x = 3(y - )² -
→ Add to both sides
∴ x + = 3(y -
)²
→ Divide both sides by 3
∵ = (y -
)²
→ Take √ for both sides
∴ ± = y -
→ Add to both sides
∴ ± +
= y
→ Replace y by (x)
∴ (x) = ±
+
∴ The inverse of f(x) is (x) = ±
+
( - 6, 0).(2, 0 ) , vertex = ( - 2, - 16)
to find the x-intercepts set f(x) = 0
x² + 4x - 12 = 0
(x + 6)(x - 2) = 0 ( equate each factor to zero and solve for x )
x + 6 = 0 ⇒ x = - 6
x - 2 = 0 ⇒ x = 2
x- intercepts are ( - 6, 0),(2, 0)
given the quadratic in standard form : y = ax² + bx + c
the x-coordinate of the vertex = -
here a = 1 , b = 4 and c = - 12
x- coordinate of vertex = - = - 2
substitute this value into the equation for y-coordinate
x = - 2 → y = 4 - 8 - 12 = - 16
vertex = ( - 2, - 16)