What are the vertex and x-intercepts of the graph of y= x2 - 6x - 7?Selectone answer for the vertex and one for the x-intercepts.
A. x-intercepts: (1,0), (7,0)
B. Vertex: (3,-16)
C.Vertex: (-3,20)
D. Vertex: (3, 20)
E. x-intercepts: (-1,0). (7.0)
F. x-intercepts: (1.0), (-7,0)

Answers

Answer 1

Answer:

The vertex and $x-$ intercepts of the graph of $y= x^2 - 6x - 7$ will be $(3,-16)$ and $(7,-1)$ , respectively.

What are vertex and $x-$ intercepts of the graph?

A vertex in a quadratic equation is the minimum or maximum point of the equation and an $x-$ intercept of a graph is the point at which the graph intersects the $x-$ axis.

Vertex form, $y=a(x-h)^2+k$

We have,

$y= x^2 - 6x - 7$

Now,

Find the $x-$ intercept and to find $x-$ intercept put $y=0$ ;

i.e. $y= x^2 - 6x - 7$

$0= x^2 - 6x - 7$

$x^2 - 6x - 7=0$

Now using Mid-term split method find value of $x$ ;

$x^2 - 7x+1x - 7=0$

$x(x - 7)+1(x - 7)=0$

$(x - 7)(x +1)=0$

$(x - 7)=0$ ⇒ $x=7$

$(x +1)=0$ ⇒ $x=-1$

So, these are the $x-$ intercept $(7,-1)$ of the expression.

Now find the vertex using the above given formula;

$y=a(x-h)^2+k$

Rewrite in vertex form

$y= x^2 - 6x - 7$

Add and subtract $(-3)^2$ in given expression;

$y= x^2 - 6x + (-3)^2 -7 - (-3)^2$

$y = x^2 - 6x + 9 -7 - 9$

$y = x^2 - 6x + 9 -16$

Now convert quadratic part of equation in $(a-b)^2$ ;

$y = (x-3)^2-16$

Now compare it with $y=a(x-h)^2+k$

We get, $h=3,\ k=-16$

So, these are the vertex $(3,-16)$ of expression.

Hence, we can say that the vertex and $x-$ intercepts of the graph of $y= x^2 - 6x - 7$ will be $(3,-16)$ and $(7,-1)$ , respectively.

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Answer 2

Answer: The answer is B and E

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