Question

Function: y = x2 + 5x - 7 Vertex:( Solutions:( and

Answer 1

I can assume that we want to find the roots and the vertex of the quadratic equation:

y = x2 + 5x - 7

For a general quadratic equation of the form:

y = a*x^2 + b*x + c

The x-value of the vertex is given by:

x = -b/2a

And to get the y-value, we just need to evaluate the quadratic function in the x-value of the vertex.

Also, for that general quadratic equation, we define the zeros as the x-values at which the graph of the function intersects the x-axis.

These are solutions of:

0 = a*x^2 + b*x + c

These are given by  Bhaskara's formula:

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

Now that we know this, let's solve the problem.

First, let's find the vertex.

The function is:

y = x^2 + 5*x - 7

Then the x-value of the vertex is:

x = -5/2*1 = -(5/2)

to get the y-value of the vertex, we need to evaluate the function in the above x-value:

y = (-5/2)^2 + 5*(-5/2) - 7 = -13.25

Then the vertex is: (-(5/2), -13.25)

Now let's find the roots, we just need to solve the Bhaskara's formula:

$x = \frac{-5\pm \sqrt{5^2 - 4*1*(-7)} }{2*1} = \frac{-5 \pm 7.28}{2}$

Then the two roots are:

x = (-5 - 7.28)/2 = -6.14

x = (-5 + 7.28)/2 = 1.14

Concluding, we found that the vertex is (-(5/2), -13.25), and the roots are:

x = -6.14

x  = 1.14

In the image below you can see the graph of the question, where you also can see the vertex and the two roots.

If you want to learn more about quadratic equations, you can read:

brainly.com/question/24326986

Answer 2

Answer:=7x−7

Explanation:

=2x+5x+−7

=(2x+5x)+(−7)

=7x+−7