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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 29 Page 159

Identify the coordinates of the vertex.

y=2x^2-3

Practice makes perfect

We want to write the equation of the given parabola. To do so, let's recall the vertex form of a quadratic function. y= a(x- h)^2+ k In this expression, a, h, and k are either positive or negative constants. Let's start by identifying the vertex.

The vertex of this parabola has the coordinates ( 0, -3). This means that we have h= 0 and k= -3. We can use these values to partially write our function. y= a(x-( 0))^2+( -3)) ⇕ y= ax^2-3 We can see in the graph that the parabola opens upwards. Therefore, a will be a positive number. To find its value, we will use a point that lies on the parabola. Let's choose the point (1,- 1).

Since this point is on the curve, it satisfies its equation. Therefore, to find the value of a, we can substitute 1 for x and -1 for y, and simplify.

y=ax^2-3

x= 1, y= - 1

- 1=a( 1)^2-3

▼

Solve for a

1^a=1

- 1=a * 1-3

Identity Property of Multiplication

- 1=a-3

LHS+3=RHS+3

2 = a

Rearrange equation

a= 2

We found that a= 2. Now, we can complete the equation of the curve. y= 2x^2-3

Subchapter links

1 Graphing Quadratic Functions p.158

2 Solving Quadratic Equations by Graphing p.158

3 Transformations of Quadratic Functions p.159

4 Solving Quadratic Equations by Completing the Square p.159

5 Solving Quadratic Equations by Using the Quadratic Formula p.160

6 Analyzing Functions with Successive Differences p.160

7 Special Functions p.160