Exercise 17 Page 224

Before we try to write the equation of a specific parabola that passes through some given points, let's make sure we have enough points. We will need at least three. (0,3),(1,10),(2,19) To use the given points, we need to substitute their ( x, y) coordinate pairs into the standard form of a quadratic equation. y=a x^2+b x+c, a≠ 0 Doing so will create a system of equations that we can solve for the values of a, b, and c. Let's start with (0,3).

We already found that c=3! y=ax^2+bx+3 Now we can use (1,10) to write our second equation.

To find another equation, we will use (2,19).

We now have a system of two equations. a+b=7 & (I) 2a+b=8 & (II) Let's solve this system using the Elimination Method. We will start by subtracting Equation (I) from Equation (II) to eliminate the b-variable.

We found that a=1. y=1x^2+bx+3 ⇔ y=x^2+bx+3 Let's now substitute 1 for a in Equation (I).

Now that we have all three values, we can complete the standard form equation of the parabola that passes through the given points. y=1x^2+6x+3 ⇔ y=x^2+6x+3 To help visualize this graph, we have plotted the given points and sketched the curve below.