algebra 2 porabola

Question

so the question is

what are the zeros of the porabola on the grid? wright an equation for the graph

im not sure how to add a picture to this question i will tell you what it looks like

the porabolas vertex ( i think its the vertex) is at (-2,-4)

and its opening up

it crosses the x axis at (0,-5) on the left side and (0,-3) on the right side

Answer 1

I think you have your x's and y's mixed around. An ordered pair is (x, y) where the first number is the x and the second number is the y.

I THINK you mean that the places the parabola crosses the x-axis are (-5, 0) and (-3, 0) and that the vertex is at the point (-4, -2). So the parabola looks like this:

Based on that assumption, I can answer the question.

The zeroes are the places the parabola crosses the x-axis. So, the zeros are x = -5 and x = -3

The equation of the parabola can be determined using the vertex form of a quadratic function which is

y = a(x - h)² + k where the point (h, k) is the vertex and the value "a" is the stretch factor. we can plug in the vertex values (h and k) to get:

y = a(x - -4)² + -2 or

y = a(x + 4)² - 2

To calculate the value of "a", we can plug in one of the ordered pairs we have from the zeros, I'll pick (-5, 0). So we plug in x = -5 and y = 0 to get:

0 = a(-5 + 4)² - 2

2 = a(-1)²

2 = a

So the equation for the parabola is y = 2(x + 4)² - 2