a)
h(x) =x²-8x+21
h(x) =(x² -8x +16) +5
h(x) =(x-4)² +5
Compare with standrad form h(x) =a(x-h)² +k to obatin vertex (h, k) as
(4,5)
b)
h(x) = 0
x²-8x+21 =0
c)
h(x) has two complex zeroes, as both contain imaginary term i.
6. Given h(x) x2-8x+ 21 a. What is the vertex of the parabola? b. What are...
In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = -4(x+7)2+9 The vertex is _______ (Type an ordered pair.) Find the zeros for the polynomial function and give the multiplicity for each zero touches the x-ain and turns around at each zero. f(x) = - 7(x - 5)(x+ 9)3
Write down the equation of given parabola x? +8x+4y+12 =0 in standard form. State the vertex, focus and the equation of the directrix. Hence, sketch its graph. 4. Show that y² + 4y +8x + 12 = 0 represents a parabola. Hence, determine its focus, and directrix. [4 marks]
Consider the parabola given by the equation y = −x^2 + 8x + 3 (a) Find the vertex (x, y) (b) Solve −x^2 + 8x + 3 = 0. Round your answers to two decimal places.
For the function below, (a) find the vertex; (b) find the axis of symmetry: (c) determine a minimum value and find that value; and (d) graph the function. f(x) = x2 + 8x + 17 (a) The vertex is (Type an ordered pair, using integers or fractions.) (b) The axis of symmetry is (Type an equation. Use integers or fractions for any numbers in the equation.) (c) Does f(x) have a maximum or a minimum value? The parabola f(x) has...
DETAILS Find a function whose graph is a parabola with the given vertex and that passes through the given point. Write your answer in vertex form: f(x)-a(x-)P+* Vertex (-2, -3); passes through the point (-1,-6) f(x) DETAILS Solve the problem. The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 144 feet in 3 seconds, how far will it fall in 5 seconds? ft
Given the graph of the parabola below, with vertex at the origin and the point (4, 12) on the parabola, find the equation and directrix of the parabola. 18+ 16 14 (4, 12) 12 10- 1 8 6 4 2 - 4 -2 0 2. A) equation: y = -22, directrix: Y 1 B) equation: y = - 1x, directrix: y = 3 C) equation: y = x2, directrix: Y ساده Type here to search EI 6 2 2 -4...
16 For the quadratic function f(x) = -x2 - 8x, answer parts (a) through (c) (a) Graph the quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and X-intercepts, if any. Does the graph off open up or down? 12 8- up Odown 2015 12 118 12 16 What are the coordinates of the vertex? The vertex of the parabola is (Type an ordered pair. Use integers or fractions...
identify the vertex on no.6 Find an equation of the parabola. f(x) = у 10 X -10 5 10 (0,-4) (-2,-8) -101 6. [-/3 Points] DETAILS Write the quadratic function in a(x-h)^2+k form. f(x) = (x - 6)² + 9 f(x)= Sketch its graph. 20 16 14 12 10 8 8 4 2 . -20 -18 -16 -14 -12 -10 - -8 4 -2 2 6 8 10 12 14 16 18 20 -2 No Solution -6 -8 -10 -12...
please answer all questions For the function below. (a) find the vertex: (b) find the axis of symmetry: (c) determine whether there is a minimum value and find that value; and (d) graph the function. 17 f(x) = - X2 - 10x-24 (a) The vertex is (Type an ordered pair, using integers or fractions.) (b) The axis of symmetry is (Type an equation. Use integers or fractions for any numbers in the equation.) (C) Does f(x) have a maximum or...
Evaluate the function f(x) = x2 - 8x - 7 at the given values of the independent variable and simplify. a. f(6) b. f(x +9) c. f(-x) a. f(6)= (Simplify your answer.)