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2 years ago

What is the vertex and x-intercepts of the graph of the function below y=x^2-6x-7

Mathematics

2 answers:

labwork [276]2 years ago

6 0

Answer: The vertex is (3, 16) and the x-intercepts are (-1, 0) and (7, 0).

Step-by-step explanation: We are given to find the vertex and x-intercepts of the graph of the following function :

$y=x^2-6x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)$

We know that

the vertex of the graph of function $y=a f(x-h)^2-k$ is given by (h, k).

From equation (i), we have

$y=x^2-6x-7\\\\\Rightarrow y=(x^2-6x+9)-7-9\\\\\Rightarrow y=(x-3)^2-16.$

Therefore, the vertex is (3, 16).

The x-intercepts of function (i) will be given by

$x^2-6x-7=0\\\\\Rightarrow x^2-7x+x-7=0\\\\\Rightarrow x(x-7)+1(x-7)=0\\\\\Rightarrow (x+1)(x-7)=0\\\\\Rightarrow x+1=0,~~x-7=0\\\\\Rightarrow x=-1,~~x=7.$

Thus, the vertex is (3, 16) and the x-intercepts are (-1, 0) and (7, 0).

Strike441 [17]2 years ago

4 0

Answer:

x=(7,0),(-1,0) y=(0,-7)

Step-by-step explanation:

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4 Consider the triangle below.

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<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

$= \tt x + 1.4 = 2x + 0.1$

$= \tt x + 1.4 - 0.1 = 2x$

$= \tt \: x + 1.3 = 2x$

$= \tt 1.3 = 2x - x$

$\color{plum} \hookrightarrow \tt x = 1.3$

Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

$= \tt x + 1.4$

$= \tt 1.3 + 1.4$

$\color{plum} \tt leg \: AM= 2.7 \: inches$

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

$= \tt 2x + 0.1$

$= \tt2 \times 1.3 + 0.1$

$= \tt 2.6 + 0.1$

$\color{plum} \tt\: leg \:MG = 2.7 \: inches$

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

$= \tt 3x - 0.4$

$= \tt 3 \times 1.3 - 0.4$

$= \tt 3.9 - 0.4$

$\color{plum}\tt \: Base \: AG = 3.5 \: inches$

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

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