Question

Sketch the graph of y=(x-5) squared +3

Answer 1

Answer:

Part 1) The turning point is (5,3)

Part 2) The y-intercept is the point (0,28)

Part 3) The graph don't cross the x-axes

Part 4) The graph in the attached figure

Step-by-step explanation:

Part 1) State the turning point

we know that

A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising)

we have

$y=(x-5)^2+3$

This is the equation of a vertical parabola written in vertex form

The parabola open upward

The vertex represent a minimum

The vertex is the point (5,3)

therefore

The turning point is (5,3)

Part 2) Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

$y=(0-5)^2+3\\y=28$

The y-intercept is the point (0,28)

Part 3) Find the x-intercepts of the quadratic equation

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

$(x-5)^2+3=0$

$(x-5)^2=-3$

Remember that

$i=\sqrt{-1}$

so

$(x-5)=\pm\sqrt{-3}$

$(x-5)=\pm i\sqrt{3}$

$x=5\pm i\sqrt{3}$

The graph don't cross the x-axes

Part 4) The graph in the attached figure