Write the equation of the parabola that passes through the points shown in the table.x y1 03 04 –4Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.
Question
Write the equation of the parabola that passes through the points shown in the table.x y1 03 04 –4Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.
Solution
To find the equation of the parabola that passes through the points (1,0), (3,0), and (4,-4), we can use the form y=a(x–p)(x–q), where p and q are the x-intercepts of the parabola.
Step 1: Identify the x-intercepts From the points given, we can see that the parabola crosses the x-axis at x=1 and x=3. So, p=1 and q=3.
Step 2: Substitute the x-intercepts into the equation This gives us y=a(x–1)(x–3).
Step 3: Find the value of a To find a, we can substitute one of the points into the equation. Let's use the point (4,-4). This gives us -4=a(4-1)(4-3).
Solving for a gives a=-4.
So, the equation of the parabola is y=-4(x–1)(x–3).
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