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Q6.

Expert-verified

Algebra 1

Found in: Page 592

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.
The expression $b^{2} - 4 a c$ is called the discriminant.

The sentence, “The expression $b^{2} - 4 a c$ is called the discriminant. ” is true.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Define an expression.

A mathematical expression is a combination of numbers and variables ordered with mathematical operations.

Step 2. Define the standard form of the quadratic equation.

A quadratic equation, which is written in the form, $a x^{2} + b x + c = 0$ , where, $a \neq 0$ is called the standard form of the quadratic equation.

Step 3. Check whether the given sentence is true or false.

For the quadratic equation $y = a x^{2} + b x + c$ ,

The quadratic formula is given by

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

In this formula, the expression under the radical sign, $b^{2} - 4 a c$ , is called the discriminant.

Therefore, the sentence, “The expression $b^{2} - 4 a c$ is called the discriminant. ” is true.

Most popular questions for Math Textbooks

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Jason is playing games at a family fun center. So far he has won 38 prize tickets. How many more tickets would he need to win to place him in the gold prize category?

Number of Tickets	Prize Category
$1 - 20$	bronze
$21 - 40$	silver
$41 - 60$	gold
$61 - 80$	platinum

F $2 \leq t \leq 22$

G $3 \leq t \leq 22$

H $1 \leq t \leq 20$

J $3 \leq t \leq 20$

Solve each equation by completing the square. Round to the nearest tenth if necessary.

$y^{2} - 8 y + 16 = 36$

Find the next three terms in each geometric sequence.

$32, 8, 2 .....$

OPEN ENDED Write a quadratic function for which the graph has an axis of symmetry $x = - \frac{3}{8}$ . Summarize your steps.

The population of bacteria in a petri dish increases according to the model $p = 550 {(2 .7)}^{0 .008 t}$ , where $t$ is the number of hours and $t = 0$ corresponds to $1 : 00 P . M$ . Use this model to estimate the number of bacteria in the dish at $5 : 00 P . M$ .

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