Use the function f(x) to answer the questions: f(x) = 5x2 + 2x − 3 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Part A : As you know, the x - intercept is a point with which the y - coordinate has a value of 0. f( x ) can otherwise be known as 0, so to determine the x - intercept, you would have to solve the following equation,

5x² + 2x − 3 = 0,

( 5x - 3 )( x + 1 ) = 0,

5x - 3 = 0 ⇒ x = 3 / 5,

x + 1 = 0 ⇒ x = - 1

As you can see there are two solutions to this quadratic equation, x = 3 / 5, and x = - 1. Therefore, there will be two points with which the graph meets the x - axis, ( , 0 ) and ( - 1, 0 ).

Part B : We can tell that the vertex of this graph is going to be a minimum, as it is a up - down facing parabola. It is such as it is in the form y = ax² + bx + c. However, let's check the coordinates of our vertex.

The parabola parameters are a = 5, b = 2, and c = - 3,

, respectively,

, therefore the vertex will be at point .

Part C : We know the vertex is at point  , and the x- intercepts are ( , 0 ) and ( - 1, 0 ). Therefore we can simply draw a curved line intersecting these points, creating our graph.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.