Exercise 18 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. (0,0),(1,- 5),(2,0) 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 (0,0).

We already found that c=0. y=ax^2+bx+0 ⇔ y=ax^2 +bx Now we can use (1,- 5) to write our second equation.

To find another equation, we will use (2,0).

We now have a system of two equations. a+b=- 5 & (I) 2a+b=0 & (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=5. y=5x^2+bx Let's now substitute 5 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=5x^2+(- 10)x ⇕ y = 5x^2-10x To help visualize this graph, we have plotted the given points and sketched the curve below.