Question

Consider the graph y = 2x2 + 7x + 6.

a) The graph of this equation is called a parabola. Does this parabola open
upward or downward? How do you know?

b) What is the y-intercept? How do you know?

c) Find the x-intercepts. Show relevant process.

Answer 1

a) Parabola opens up

b) 6

c) -3/2 and -2

Explanation:

a) The general form of a parabolic graph is;

y = ax^2 + bx + c

if a is positive, it faces up, if negative, it opens down

Since a = 2 here, it is positive and thus the parabola faces or opens up

b) The y-intercept is simply the c term

the value here is 6

The y intercept is obtained when the x value is zero

So by simply setting the x value to zero, we can easily get the y value since x is zero at that point

c) The x-intercepts refer to the roots of the equation

By solving the quadratic equation i.e substituting 0 for y, we can get the two x values as follows;

2x^2 + 7x + 6 = 0

2x^2 + 4x + 3x + 6 = 0

2x(x + 2) + 3(x + 2) = 0

(2x + 3)(x + 2) = 0

2x + 3 = 0 or x + 2 = 0

2x = -3 or x = -2

x = -3/2 or x = -2