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Home Question Bank Math Algebra Archive 2025 February 15

Algebra Questions from Feb 15,2025

Browse the Algebra Q&A Archive for Feb 15,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Enunciado Despeja \( y \) en la ecuación \( 2 x+3 y=6 \) : Solve for \( k: \quad \frac{k}{3}-\frac{5}{k+2}=4 \) Find the following for the function \( f(x)=3 x^{2}+4 x-2 \). \( \begin{array}{llll}\text { (a) } f(0) & \text { (b) } f(1) & \text { (c) } f(-1) & \text { (d) } f(-x) \\ \text { (e) }-f(x) & \text { (f) } f(x+1) & \text { (g) } f(4 x) & \text { (h) } f(x+h)\end{array} \) \( 3^{2 x}-1=18^{x}+6 \) Solve for \( x \) : Enunciado Simplifica la expresión \( 2 x+3 x-5 \) Find the vertex, axis of symmetry and \( y \)-intercept of the associated parabola, \[ f(x)=10 x^{2}+20 \] Vertex: \( \square \) \( \square \) Axls of symmetry: \( \square \) \( y \)-intercept: \( (0 \), \( \square \) Question Help: Video eBook Written Example Find the vertex, axis of symmetry and \( y \)-intercept of the associated parabola. \( f(x)=-x^{2}+x+5 \) Vertex: Axis of symmetry: \( y \)-intercept: \( (0 \), \( \left. \begin{array} { l l l } { 7 y = 28 } & { y = \square } \\ { y + 5 = 18 } & { y = \square } \\ { - 2 + y = - 5 } & { y = \square } \\ { \frac { y } { 3 } = 6 } & { y = \square } \end{array} \right. \) Find the vertex, axis of symmetry and \( y \)-intercept of the associated parabola. \( f(x)=2 x^{2}+4 x+4 \) Vertex: Axis of symmetry: \( y \)-intercept: \( (0, \square) \) Find the discriminant and use it to determine the number of \( x \)-intercepts of the graph of \( f \). Also, determine the number of real solutions to the equation \( f(x)=0 \). \( f(x)=x^{2}-2 x+3 \) Discriminant: Which means there are \( \square x \)-intercept(s) and there are \( \square \) \( f(x)=0 \).
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