Find the vertex of the parabola
y = f(x)= x^2 + 8 x - 11
x coordinate =
y coordinate =
Graph this function and estimate the x intercepts to the nearest tenth. Give your answers in order.
x intercept one =
x intercept two =
To find the vertex of a parabola in the form of y = ax^2 + bx + c, you can use the formula x = -b/2a to find the x-coordinate of the vertex. Then plug this value into the equation to find the corresponding y-coordinate.
In the given equation y = x^2 + 8x - 11, we have a = 1, b = 8, and c = -11. Using the formula x = -b/2a, we can calculate:
x-coordinate = -8/(2*1) = -8/2 = -4
To find the y-coordinate, substitute the x-coordinate (-4) into the equation:
y-coordinate = (-4)^2 + 8*(-4) - 11 = 16 - 32 - 11 = -27
Therefore, the vertex of the parabola is (-4, -27).
To graph the function and estimate the x-intercepts, we can plot some points on the graph. We can calculate the y-values for various x-values and check where the graph intersects the x-axis (y = 0).
Using the quadratic formula or factoring, we can find the x-intercepts of the parabola.
Using the formula x = (-b ± √(b^2 - 4ac))/2a, we can calculate the x-intercepts:
x intercepts = (-8 ± √(8^2 - 4*1*(-11)))/2*1
= (-8 ± √(64 + 44))/2
= (-8 ± √108)/2
= (-8 ± √(36*3))/2
= (-8 ± 6√3)/2
= -4 ± 3√3
Therefore, the estimated x-intercepts to the nearest tenth are:
x intercept one = -4 + 3√3 ≈ 0.2 (rounded to the nearest tenth)
x intercept two = -4 - 3√3 ≈ -8.5 (rounded to the nearest tenth)
To plot the graph of the function, mark the vertex (-4, -27) and the x-intercepts (0.2, 0) and (-8.5, 0) on a graph. Draw a U-shaped curve passing through these points.
Y = x^2 + 8x - 11
h = Xv = -B/2A = -8/2 = -4.
k = Yv = (-4)^2 + 8*(-4) - 11 = -27
V(h, k) = (-4,-27)
Use the following points for graphing:
(x, y).
(-10,9)
(-7,-18)
(-6,-23)
(-5,-26)
V(-4,-27)
(-3,-26)
(-2,-23)
(-1,-18)
(2,9).
X-intercepts:
X1 will be negative.
X2 will be positive.