Exercise 26 Page 594

We are asked to write a quadratic function whose graph passes through the given points. (0,7), (2,13), (4,35) 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 Doing so will create a system of equations that we can solve for the values of a, b, and c. Let's start with (0,7).

Not only did we write our first equation, but we also solved it! Now let's write an equation using (2,13).

To find our third and last equation, we will use (4,35).

We now have a system of three equations. c=7 & (I) 4a+2b+c=13 & (II) 16a+4b+c=35 & (III) Since Equation (I) is already solved for c, we will start by substituting the value of c into Equation (II) and Equation (III).

Now we will continue solving using the Elimination Method. We will start by multiplying Equation (II) by 2. Then we will subtract Equation (II) from Equation (III) to eliminate the b-variable.

Let's substitute 2 for a in Equation (II) to find the value of b.

Now that we have all three values, we can write the equation of the quadratic function whose graph passes through the given points. y=2x^2+(- 1)x+7 ⇔ y=2x^2-x+7 To help visualize the graph, we have plotted the given points and sketched the curve below.