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Find point \( G \) on \( \overline{A B} \) such that the ratio of \( A G \) to \( G B \) is 3:2

\( f(x)=3 x^{2}+12 x-6 \) (a) The function's vertex is at the point \( (-2,-18) \) (Type an ordered pair, using integers or fractions.) (b) Determine whether the parabola has a maximum value or a minimum value and find the value Select the correct choice below and fill in the answer (Type an integer or a fraction.) A. The parabola opens downward and has a maximum value of B. The parabola opens upward and has a minimum value of -18 (c) The range of \( f(x) \) is \( [-18, \infty) \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) (d) The function is increasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

A ball is thrown directly upward from a height of 7 ft with an initial velocity of \( 24 \mathrm{ft} / \mathrm{sec} \). The function \( \mathrm{s}(\mathrm{t})=-16 \mathrm{t}^{2}+24 \mathrm{t}+7 \) gives the height of the ball, in feet, t seconds after it has been thrown. The ball reaches its maximum height of (Simplify your answers. Type integers or decimals.)

Which of the following describes a facility where patients live with healthcare professionals? A facility for patients who cannot live independently A facility where a patient stays while they undergo rehabilitation therapy A clinical setting where patients receive outpatient medical care A clinical setting designed to treat minor acute conditions

\( F(x)=-4 x^{2}+5 \) Hallar \( F(x+h \) \( -4(x+h)^{2}+5 \) \( -4\left(x^{2}+2 \cdot x \cdot h+h^{2}\right)+5 \) \( -4 x^{2}-8 \cdot x \cdot h-4 h^{2}+5 \) Hallar \( -F(x) \) \( \quad+4 x^{2}-5 \) juntamog \( 1 y^{2} \) \( -4 x^{2}-8 \cdot x \cdot h-4 h^{2}+5+4 x^{2}-5 \) \( -8 \cdot x \cdot h-4 h^{2} \) Dividimos por \( h \) \( \frac{-8 \cdot x \cdot h-4 h^{2}}{h}=-8 \cdot x \cdot-4 h \) Hallar el limite -8.x. \( -4 h \) - \( 8 \cdot x-4(0) \) - \( 8 x \)