Ratio:
Which set of numbers could be the lengths of the sides of a triangle?
1 answer:
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Answer:
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).
