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What is an equation of a parabola with the given vertex and focus Vertex:(0 0) Focus: (2.5 0) View Answer A parabola with equation y = x^2 + bx + c passes through the points (2,3) and (4,3).
Since the equation is in vertex form, the vertex will be at the point (h, k). The vertex is the minimum or maximum point of a parabola. The key features of a parabola are its vertex, axis of symmetry, focus, directrix, and focal diameter. The focus of a parabola is always inside the parabola; the vertex is always on the parabola; the directrix is always outside the parabola. When given a standard equation for a parabola centered at the origin, we can easily identify the key features to graph the parabola. Find the vertex. The standard form of a parabola is #y=ax^2++bx+c#, where #a!=0#.. There are two form of Parabola Equation Standard Form and Vertex Form. A line is said to be tangent to a … Anyway, it's because the equation is actually in the conic form for a parabola. The standard form of a parabola is ( x – h) 2 = a ( y – k) or ( y – k) 2 = a ( x – h ), where ( h, k) is the vertex. The vertex form of a quadratic equation is f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. A horizontal line drawn through this vertex is the line of symmetry of a parabola. Step 3: Find the x-intercept(s). We suggest you apologize. To find the y-intercept let x = 0 and solve for y. If #a>0#, the vertex is the minimum point and the parabola opens upward.If #a<0#, the vertex is the maximum point and the parabola opens downward.. To find the vertex, you need to find the x- and y-coordinates.
We recognize h and k from the vertex form of a parabola as, well, the vertex, (h, k). A parabola is a curve where any point is at an equal distance from a fixed point (called the focus), and a fixed straight line (called the directrix). That equation is a little funny looking, although it isn't really polite to say that. The methods used here to rewrite the equation of a parabola into its standard form also apply when rewriting equations of circles, ellipses, and hyperbolas. To find the x-intercept let y = 0 and solve for x. Step 2: Find the y-intercept. The "general" form of a parabola's equation is the one you're used to, y = ax 2 + bx + c — unless the quadratic is "sideways", in which case the equation will look something like x = ay 2 + by + c. That's the form: 4p(y – k) = (x – h) 2.
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