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Chapter 3: Problem 97

Write the equation of each parabola in standard form. Vertex: \((-3,-4) ;\) The graph passes through the point \((1,4)\)

Short Answer

Expert verified
The equation of the parabola in standard form is \(y=0.5(x+3)^2-4\).

Step by step solution

01

Identify Given Details

Identify and list down the given details. The vertex of the parabola is given by \((-3,-4)\), so we know \(h=-3\) and \(k=-4\). The parabola passes through the point \((1,4)\), so \(x=1\) and \(y=4\).
02

Substitute in the Standard Parabola Equation

Substitute the given details into the standard equation. Since we don鈥檛 know the value of a yet, the equation becomes: \(4=a(1-(-3))^2-4 = a(1+3)^2-4 = a*16-4\). Solve it for \(a\), you get \(a= \frac{4+4}{16}=0.5\).
03

Formulate the Standard Form of the Parabola

Next, substitute the values of \(h\), \(k\), and \(a\) that we have identified, into the standard form equation. This gives: \(y=0.5(x-(-3))^2-4 = 0.5(x+3)^2-4\). This is the standard form equation of the parabola.

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