Ch. 3 - Polynomial and Rational Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 3 - Polynomial and Rational Functions

Problem 98

Chapter 4, Problem 98

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

Verified step by step guidance

Recall that the vertex form of a parabola's equation is given by

y = a (x - h) 2 + k

, where

(h, k)

is the vertex.

Substitute the vertex coordinates

(-3, -1)

into the vertex form equation, so it becomes

y = a(x + 3)^2 - 1

Use the given point

(-2, -3)

that lies on the parabola to find the value of

a

. Substitute

x = -2

and

y = -3

into the equation:

-3 = a(-2 + 3)^2 - 1

Simplify the equation from step 3 to solve for

a

. Calculate the squared term and isolate

a

on one side.

Write the final vertex form equation by substituting the found value of

a

back into

y = a(x + 3)^2 - 1

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vertex Form of a Parabola

The vertex form of a parabola's equation is y = a(x - h)^2 + k, where (h, k) is the vertex. This form makes it easy to identify the vertex and understand the parabola's shape and position on the coordinate plane.

Using a Point to Find 'a'

After writing the vertex form with the known vertex, substitute the coordinates of a given point on the parabola into the equation to solve for the coefficient 'a'. This determines the parabola's width and direction (upward or downward).

Graph Interpretation and Coordinate Substitution

Understanding how to interpret points on the graph and substitute their coordinates into an equation is essential. This process connects the geometric representation of the parabola with its algebraic equation.

Recommended video:

Guided course

02:16

Graphs and Coordinates - Example

Related Practice

Textbook Question

Exercises 107–109 will help you prepare for the material covered in the next section. Factor: x³+3x²−x−3

Textbook Question

Use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x) = (2x+7)/(x+3)

Textbook Question

Solve: $x^{4} - 6 x^{3} + 4 x^{2} + 15 x + 4 = 0$ .

views

Textbook Question

Find the average rate of change of f(x)=√x from x₁=4 to x₂=9.

Textbook Question

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).

views