Answer:
f(x) = 4(x + 6)² – 134
Step-by-step explanation:
To write an equation in vertex form, we first factor out the GCF of the first two terms. For 4x² and 48x, this is 4:
f(x) = 4(x²+12x)+10
Next we complete the square. The value of b inside parentheses is 12; we take half of that and square it:
(12/2)² = 6² = 36
We add this inside parentheses. However in order to preserve equality, we must subtract this value as well. Since the terms inside parentheses are being multiplied by 4, we multiply the 36 we subtract by 4 as well:
f(x) = 4(x²+12x+36)-4(36)+10
Simplifying, we have
f(x) = 4(x²+12x+36)-144+10
Combining like terms,
f(x) = 4(x²+12x+36)-134
Next we write the trinomial in parentheses as a perfect square:
f(x) = 4(x+6)²-134
Answer:
The solution set is (-3, 4).
Step-by-step explanation:
x2 + 4x - 9 = 5x + 3
x^2 + 4x - 5x - 9 - 3 = 0
x^2 -x - 12 = 0
(x - 4)(x + 3) = 0
x = -3, 4.
Answer:
The graph is in the image
Step-by-step explanation:
Answer:
x = - 4, x = 0, x = 1
Step-by-step explanation:
To find the zeros equate p(x) to zero, that is
3x³ + 9x² - 12x = 0 ← divide through by 3
x³ + 3x² - 4x = 0 ← factor out x from each term
x(x² + 3x - 4) = 0
x(x + 4)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x = 0
x + 4 = 0 ⇒ x = - 4
x - 1 = 0 ⇒ x = 1
Area of square = Side × side
= 1 6/7 × 1 6/7
= 3.45 square millimeters
