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.

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i believe the answer is letter c) 8

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