A function is shown:

f(x) = x² + 2x - 3

Show the x-intercepts and maximum or minimum of the function.

f(x) = x² + 2x - 3

Show the x-intercepts and maximum or minimum of the function.

**To find the x-intercepts, replace f(x) with zero and solve the equation for x.**

f(x) = x² + 2x - 3

x² + 2x - 3 = 0 {replaced f(x) with 0, because at the x-intercept, y is equal to 0}

(x + 3)(x - 1) = 0 {factored into two binomials}

x + 3 = 0 or x - 1 = 0 {set each factor equal to 0}

x = -3 or x = 1 {solved the equations for x}

**The x-intercepts are -3 and 1.**

The coefficient of x² is positive, therefore the parabola opens upward. Thus, the function has a minimum value.

The maximum or minimum value of the function is the y-coordinate of the vertex.

**The x-coordinate of the vertex is:**

-b

----

2a

In f(x) = x² + 2x - 3,

a = 1, b = 2, and c = -3 {a is the coefficient of x², b is the coefficient of x, and c is the constant term}

-b

---- {the x-coordinate of the vertex}

2a

-2

= ----- {substituted 2 for b and 1 for a}

2(1)

= -1 {simplified}

**The x-coordinate of the vertex is -1.**

**To find the y-coordinate of the vertex, substitute -1, in for x, into the function.**

f(-1)

= (-1)² + 2(-1) - 3 {substituted -1/4 in for x}

= 1 - 2 - 3 {evaluated exponent and multiplied}

= -4 {subtracted}

The y-coordinate of the vertex is -4.

**The minimum value of the function is -4.**