Questions: Determine the equation of the parabola whose graph is given below. Enter your answer in general form.

Transcript text: Determine the equation of the parabola whose graph is given below. Enter your answer in general form.

Solution

Solution Steps

Step 1: Determine the vertex of the parabola

The vertex is the highest or lowest point on the parabola. In this case, the vertex is (2, 1).

Step 2: Determine another point on the parabola

We can choose the x-intercept (3, 0).

Step 3: Write the equation in vertex form

The vertex form of a parabola is $y = a(x-h)^2 + k$, where (h, k) is the vertex. Plugging in the vertex (2, 1), we get $y = a(x-2)^2 + 1$.

Step 4: Solve for _a_

Substitute the other point (3, 0) into the equation: $0 = a(3-2)^2 + 1$. Simplifying this, we get $0 = a(1)^2 + 1$, so $0 = a + 1$. Solving for $a$, we get $a = -1$.

Step 5: Write the equation in vertex form

Substitute $a = -1$ back into the vertex form: $y = -(x-2)^2 + 1$.

Step 6: Expand to general form

Expand the equation: $y = -(x^2 - 4x + 4) + 1$ $y = -x^2 + 4x - 4 + 1$ $y = -x^2 + 4x - 3$

Final Answer: The equation of the parabola in general form is $y = -x^2 + 4x - 3$

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