AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Write the equation in vertex form for the parabola with vertex and focus .Simplify any fractions.______
Full solution
Q. Write the equation in vertex form for the parabola with vertex and focus .Simplify any fractions.______
- Identify Parabola Direction: Vertex: Focus: Identify the direction of the parabola.Since the focus is above the vertex, the parabola opens upwards.
- Vertex Form Explanation: Vertex form of an upward parabola: Here, is the vertex.
- Calculate Value of a: Calculate the value of a.The distance between the vertex and focus is |(-3) - (-1)| = 2＂).\(\newlineSince the parabola opens upwards, \$a\) is positive.\(\newline\)\(a = \frac{1}{4p}\), where \(p\) is the distance between the vertex and focus.\(\newline\)\(a = \frac{1}{4\times 2} = \frac{1}{8}\).
- Substitute Values into Equation: Substitute the values of \(h\), \(k\), and \(a\) into the vertex form equation.\(h = 0\), \(k = -3\), \(a = \frac{1}{8}\).\(y = \frac{1}{8}(x-0)^2-3\)\(y = \frac{1}{8}x^2-3\)
