Having two roots y intercept -1 and with vertex (-1,22)

    Vertex form: y = -23(x + 1)² + 22  

Standard form: y = -23x² - 46x - 1

Roots at (-1.978, 0) and (-0.022, 0)

Step-by-step explanation:

The vertex form of the equation for a parabola is

y = a(x - h)² + k

where h and k are the coordinates of the vertex  and a is a constant.

Data:

Vertex at (-1,22)

y-intercept at (0, -1)

Calculations:

1. Substitute the coordinates of the vertex into the equation

y = a(x + 1)² + 22

2. Substitute the coordinates of the y-intercept into the equation and solve for a

The equation of the parabola in vertex form is

y = -23(x + 1)² + 22

To convert the equation to standard form, you expand the vertex form.

The equation of the parabola in standard form is

y = -23x² - 46x - 1

3. Find the roots

The roots are the values of x that make y = 0

The roots are at x = -1.978 and x = -0.022.

The graph shows your parabola with vertex (-1, 22), y-intercept at (0, -1). and x-intercepts at (-1.978, 0) and (-0.022, 0).

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step-by-step explanation:

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step-by-step explanation: