Question

Without graphing, state the vertex for each of the following quadratic equations.

Answer 1

Answer:

$(5,3)$

$(0,-2.5)$

$(-4,0)$

Step-by-step explanation:

The equation of a parabola in the form of the vertex is the following:

$y=a(x-h)^2+k$

and the vertex will be in the coordinates: $(h,k)$

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

we can see that $h=5$, and $k=3$

so the vertex is at $(5,3)$

for b. $y =x^2 - 2.5$

we can re accommodate this equation as: $y=(x-0)^2+(-2.5)$

in this form is easier to see that $h=0$, and $k=-2.5$

so the vertex is at $(0,-2.5)$

for c. $y = (x + 4)^2$

we can re accommodate this equation as: $(x-(-4))^2+0$

and as we can see $h=-4$ and $k=0$

so the vertex is at $(-4,0)$