Graphs：練習問題

A point is plotted on a coordinate grid in the second quadrant.
Which of the following coordinates could represent this point?

A quadratic function is given by the equation \( y = x^2 - 4x + 3 \).
By factorising the expression or otherwise, identify the roots of the function where the graph crosses the \( x \)-axis.

The straight line \(y = x + 2\) intersects the curve \(y = x^2 - 4\) at two points.
Find the positive \(x\)-coordinate of the point of intersection.

Which of the following is the correct equation for a straight line that is parallel to the line \( y = 2x + 7 \) and passes through the origin \( (0,0) \)?

A straight line passes through the point \( (0, 4) \) and the point \( (3, 10) \).
Find the equation of the line in the form \( y = mx + c \).

A straight line has the equation \( y = 5x + 9 \).
Write down the gradient and the coordinates of the y-intercept of this line.

A line passes through the points \(A(0, 5)\) and \(B(4, 13)\).
Find the equation of the line in the form \(y = mx + c\).

A circle has the equation \( x^2 + y^2 = 20 \).
Find the equation of the tangent to the circle at the point \( (2, 4) \).
Give your answer in the form \( y = mx + c \).

Consider the linear function \(y = 3x + 4\).

a) Complete the following table of values for this function:

\(\begin{array}{|c|c|c|c|c|} \hline x & -1 & 0 & 1 & 2 \\ \hline y & & & & \\ \hline \end{array}\)

b) Use your table to state the coordinates of the point where the graph crosses the \(y\)-axis.

Line \(L\) passes through the points \(A(2, 5)\) and \(B(4, 13)\).

a) Calculate the gradient of line \(L\).

b) Find the equation of line \(L\) in the form \(y = mx + c\).

c) A second line, \(M\), is parallel to line \(L\) and passes through the origin. Write down the equation of line \(M\).