Write the given function in vertex form and draw its graph. Write down the range of values of the given function.
Shift the graph of the function f(x) such that it touches the abscissa axis and is symmetrical with respect to the ordinate axis. Write the equation of this new graph.
.
.
:
as the sum of two numbers so that their product is 
.
intersect?
for which the graph of the function f(x) and the line with the equation 
intersect at two distinct points.
:
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.
.
.
.
as the product of two numbers whose sum is 
.
and 
.
.
and 
.
.
and the product is 
. Find the numbers.
and their sum is 
. Find the numbers.
and has zeros as 
and 
.
and the sum is 
.
if its zeros are given 
and 
, determine the real number m so that the sum of the solutions of the equation is equal to 
.
is given, where m is any real number. For which value of m will the solutions of the equation be additive inverse of each other?
and their difference is 
. Write down the numbers.
, and the side a is 
shorter than the side b. What is the measurement of a and b.
have two different real solutions?
have real solutions?
have no real solutions?
have only one solution?
and the hypotenuse measures 
. Calculate the length of the legs.
have a double solution?
. If 
is the hypotenuse, find the length of all sides.
and its graph goes through the origin.
,for what real number a will the roots of the equation, 
and 
, have the relation, 
?
.
has 
as its zeros. Write a relation for the function f and draw its graph. For what value c is the graph of the function 
symmetric with respect to the ordinate axis?
, 
, find and write the equation of parabola whose vertex is on the x-axis.
.
. Determine the sides of the the inscribed rectangle that has sides parallel to the diagonals of the square and has the largest area.
and the linear function 
. Calculate the coordinates of their points of intersections.
:
is the symmetric axis of the graph of the function f(x).
without solving the quadratic equation.
:
and 
and the y-axis at point 
.
. The sum of this fraction, the inverse fraction and 
is 
. Find the fraction.
.
.
is given, where m is any real number. For what value of m will the roots of the equation be multiplicative inverse of the other.
:
is given.
and 
and a value of 
at 
.
and - 3, and passes through the point 
.
, where 
with the vertex at point (2, 6), find the value of u and v, and hence the function f(x).
.
. Find the value of m for which the function has its vertex at the point (2, - 3).
.
and a value of 
at 
.
lies on the line 
.
.
and the value of x where it occurs.
, and reaches a maximum value of 19 at 
.
and mirror it over the coordinate axes. Draw the resulting curve in the coordinate system and write down its equation.
. At what value of x does it occurs?
. For what value of the coefficient a will the graph passes through the point T (- 1, 3)?
reaches its lowest point? What is this minimum value?
lies on the line 
.
.
.
in parallel so that the vertex of the graph is at the point T(3, - 1).
.
, one of the zeros 
and an extreme value at 
.
runs through the points 
, 
and 
. Calculate the values of 
, 
and 
and write down the rule of the function f(x).
.
in the same coordinate system.
.
and one of its zeros is 
.
.
.
.
and the line 
.
function and accurately draw graphs of both functions in the same coordinate system.
.
smaller than its inverse fraction. Find the fraction if the numerator is 7 less than the denominator?
is 
. What is the length of the diagonal of the rectangle?
is divided into a square and a rectangle as shown in the figure. What is the length of the square if the side of the rectangle is 
smaller than the side of the square?
, the distance between the centre and a chord is 
shorter than the chord of the circle. What is the length of the chord?
and area 
measure?
and 
and 
and 
.
. Newlyweds couple will have to pay 
more per person for an extra treat. If there were just two couples in the excursion, how many participants were there and how much did the other participants have to pay for it per person?
and 
.
be equal to 8.
be equal to half of the other solution .
is 1.
; 
find and write that function for which the sum of roots is 
.
and straight line 
.
and 
of the equation 
suffice if 
is true.
find k such that the sum of the solutions of 
and 
of the equation 
is equal to 
.
and 
, and has a value of 
at point 
.
and 
as zeros, and its graph goes through the point 
.
and 
, and its graph intersects the ordinate axis at 
.
and 
intersects the ordinate axis at the point 
. Write a rule for the f function, calculate the coordinates of the vertex, and draw its graph.
.
.
.
and draw its graph.
is given. Write down the zeros of the function and the coordinates of the intersection of the graph with the ordinate axis.
of the tangent of the parabola 
? Write the tangent of the line and the parabola .
.
touch the parabola 
? Obtain the points of contact of tangent of the line and the parabola.
and 
.
and 
with a denominator equal to the lowest common denominator.
is given. Draw a graph of the function f.
, the length of its hypotenuse is 
. Calculate the lengths of the sides.
and 
on the same coordinate system.
, whose graph you got, is even. Write down the number c and the expression for the function g.
and 
.
, the length of its hypotenuse is 
. Calculate the length of the sides.
is given, where m is any real number. For 
write the rule of the function f and draw its graph .
and write down the exact solution. For which numbers a does the above equation have two different real solutions?
is given. Find the equation of the tangent to the parabola that intersects the ordinate axis at 
, and write the coordinate point of intersection of the tangent.
is given:
be tangent to the graph of the function f?
of the tangent to the graph of the function 
? Draw a graph of the function f and the required tangent .
has the shape of a rectangle. You would need 
fences to enclose it. Calculate the width and length of the land.
at an angle 
relative to the horizontal ground. The time t of the grenade is described by the equation 
, where the gravitational acceleration on the Earth's surface is 
.
, 
and 
and check the result graphically.
with an initial velocity 
. The center of gravity of the arrow moves along the parabola. What is the maximum height h reached by the arrow, and what is its range d? Use the formula:
and 
are given.
is given. In the same coordinate system, draw a graph of the function f and its tangents intersecting the ordinate axis at 
.
