Q5. State whether the given sentence... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 9: Q5. (page 592)

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.
A quadratic equation with a graph that has two $x$ -intercepts has one real root.

Short Answer

Expert verified

The sentence, 鈥淭he quadratic equation with a graph that has two $x$ -intercepts has one real root 鈥� is false.

The correct replacement for the underlined term to make a true sentence is two.

Step by step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y = a x^{2} + b x + c$ , where, $a 鈮� 0$ is called the standard form of the quadratic function.

Step 2. Define the x-intercept of a function.

The $x$ -intercepts of a function $y = a x^{2} + b x + c$ are the points, where the value $y$ is equal to 0.

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

If the graph of the quadratic equation $y = a x^{2} + b x + c,$ has two intercepts, then it means that the graph cuts the -axis at two points and the equation has two real roots.

Therefore, the sentence, 鈥淭he quadratic equation with a graph that has two $x$ -intercepts has one real root 鈥� is false.

The correct replacement for the underlined term to make a true sentence is two.

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91影视

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.
A quadratic equation with a graph that has two $x$ -intercepts has one real root.

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the x-intercept of a function.

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

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91影视

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.A quadratic equation with a graph that has two x-intercepts has one real root.

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the x-intercept of a function.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Calculus

Logic and Functions

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.
A quadratic equation with a graph that has two $x$ -intercepts has one real root.