graph a parabola whose x- intercept are at x= -3 and x= 5 and whose minimum value is y= -4
you are all terrible
To graph a parabola with given x-intercepts and a minimum value, you can follow these steps:
Step 1: Identify the axis of symmetry:
Since the x-intercepts are at x = -3 and x = 5, the axis of symmetry is the average of these two values:
Axis of symmetry = (-3 + 5) / 2 = 2 / 2 = 1
Step 2: Find the vertex:
Since the vertex lies on the axis of symmetry, its x-coordinate is the same as the axis of symmetry. Plugging that x-value into the equation of the parabola will give us the y-coordinate.
y = -4 (minimum value)
Vertex = (1, -4)
Step 3: Find the coefficient for x^2:
Since the parabola has a minimum point, the coefficient of x^2 must be positive. Let's assume the coefficient is "a".
Step 4: Write the equation of the parabola:
Using the vertex form of a parabola, the equation can be written as:
y = a(x - h)^2 + k
where (h, k) represents the vertex.
Substituting the vertex coordinates, we get:
y = a(x - 1)^2 - 4
Step 5: Find the value of "a":
To find the value of "a," we can use one of the given x-intercepts along with the equation from step 4. Let's use x = -3.
Since the x-intercept is a point where y = 0, we can substitute x = -3 and y = 0 into the equation:
0 = a(-3 - 1)^2 - 4
0 = 16a - 4
16a = 4
a = 4/16
a = 1/4
Step 6: Final equation and graph the parabola:
Now that we have the value of "a," we can substitute all the values back into the equation from step 4:
y = (1/4)(x - 1)^2 - 4
By using this equation, you can plot points on the graph or use software (such as desmos.com or graphing calculators) to visualize the parabola on a coordinate plane.
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from the roots, you know that
y = a(x+3)(x-5)
The vertex lies midway between the roots, at x = 1
y(1) = a(4)(-4) = -16a = -4, so a = 1/4
Thus, since the vertex is at (1,-4)
y = 1/4 (x+3)(x-5) = 1/4 (x-1)^2 - 4
I assume you can now graph it. If not, go to any handy online graphing website.