Find the standard form, vertex, focus and directrix of the parabola given by the equation y$^2$ + 3y - 4x = -$\frac{1}{4}$ Standard form: Vertex: (-1.6, -1.5) Focus: Directrix: Graph the parabola:
Added by Gregory P.
Close
Step 1
Step 1: Rewrite the equation in standard form 9 + 8y = 4x 4x = 8y - 9 x = 2y - 9/4 Completing the square: x - 2y = -9/4 (x - 2y)^2 = 1/16(9) (x - 2y)^2 = (1/4)^2(3)^2 (x - 2y + 3/4)^2 = (1/4)^2(3)^2 + (3/4)^2 (x - 2y + 3/4)^2 = 9/16 + 9/16 (x - 2y + 3/4)^2 = Show more…
Show all steps
Your feedback will help us improve your experience
Arjun Singh and 73 other Algebra and Trigonometry educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Convert the equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. x^2 + 10x - 4y + 9 = 0
Aman G.
Find the vertex, focus, and directrix of the parabola: 9x^2 + 8y = 0. Vertex (x, y) = Focus (x, y) = Directrix Sketch its graph.
Adi S.
Convert each equation to standard form by completing the square on $x$ or $y .$ Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$x^{2}-2 x-4 y+9=0$$
Conic Sections and Analytic Geometry
The Parabola
Recommended Textbooks
Introductory and Intermediate Algebra for College Students 4th
Prealgebra
Prealgebra and Introductory Algebra
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD