Question

Please help 60 points for a 4 part question

Answer 1

Answer:

a) x = -6, 2 b) y = -12, c) minimum at y=-16

Step-by-step explanation:

y = x² + 4x - 12

The x intercepts are where the graph crosses the x-axis (y=0):

0 = x² + 4x - 12

0 = (x + 6) (x - 2)

x = -6, x = 2

The y intercept is where the graph crosses the y-axis (x=0):

y = (0)² + 4(0) - 12

y = -12

The max or min is at the vertex of the parabola, which happens at x = -b / (2a):

x = -4 / (2*1)

x = -2

At x=-2:

y = (-2)² + 4(-2) - 12

y = -16

Since the leading coefficient is positive (+1 x²), this is an upwards parabola, so the vertex is the minimum.

Answer 2

Answer:

a) The x-intercepts are (-6,0) and (2,0)

b) The y-intercept is (0,-12)

c) the minimum value is -16 and the ordered pair is (-2,-16)

Step-by-step explanation:

We can find the x-intercepts by factoring the equation

$x^2+4x-12=0\\\\(x+6)(x-2)=0\\\\x=-6,2$

We can find the y-intercept by plugging in x=0 into the equation

$x^2+4x-12\\\\0^2+4(0)-12\\\\-12$

We can find the max/min value by finding the vertex of this Parabola.

The equation that allows us to find its x value is

$x=\frac{-b}{2a}$

For this equation,

a=1

b=4

c=-12

This means that the equation would look like this

$x=\frac{-4}{2} \\\\x=-2$

Then we can plug x=-2 into the equation in order to find the ordered pair for the vertex.

$x^2+4x-12\\\\(-2)^2+4(-2)-12\\\\4-8-12\\\\-16$