what is the relationship between the vertex and the x intercepts?
606843
(h,k) are the coordinates of the vertex, p is the distance from the vertex to the focal point as measured on the axis of symmetry. x=h will be the axis of symmetry. When y=0, the resulting value of x will be the x-intercepts.
1151352
When it comes to irreducible quadratic factors, there can't be any x-intercepts corresponding to this factor, since there are no real zeros. In other words, if we have an irreducible quadratic factor, f(x), then the graph will have no x-intercepts if we graph y = f(x).
576373
['To find the x-intercept, we set y=0 and solve for x.', 'To find the y-intercept, we set x=0 and solve for y.']
417733
The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line). The x and y axes cross at a point referred to as the origin, where the coordinates are (0,0).
1092977
In this equation, the vertex of the parabola is the point (h,k) . You can see how this relates to the standard equation by multiplying it out: y=a(x−h)(x−h)+ky=ax2−2ahx+ah2+k . This means that in the standard form, y=ax2+bx+c , the expression −b2a gives the x -coordinate of the vertex.
81517
['Look for the y-intercept where the graph crosses the y-axis.', 'Look for the x-intercept where the graph crosses the x-axis.', 'Look for the zeros of the linear function where the y-value is zero.']
590006
['If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.', 'If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity.']
336305
The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line).
1129991
Finally, both quadratic and absolute value equations can either have 0, 1, or 2 x-intercepts. However, a quadratic plots a parabola (a bowl shaped curve) while an absolute value graph plots a "V" shaped graph (see below). ... The quadratic has a smooth vertex while an absolute value has a sharp vertex.
1410175
On the graph of a quadratic, whatever is happening m units to the left of the vertex, the same thing must be happening m units to the right of the vertex. Hence, symmetry!
874019
['Press Calc (2nd Trace)', 'Choose Zero (#2)', 'For the Left Bound, arrow to the left of the x-intercept and press enter.', 'For the Right Bound, arrow to the right of the x-intercept and press enter.', 'For the Guess, arrow to the x-intercept and press enter.']
874735
A line has equation y=3x+4, state the gradient and the y-intercept. The gradient is always the number in front of the x, in this case it will be 3. Whereas for the y-intercept, it will always be the value that y equates to when x=0, in this case the y-intercept is (0,4).
685360
Get the equation in the form y = ax2 + bx + c. Calculate -b / 2a. This is the x-coordinate of the vertex. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
1155315
There are a few different ways to find the x-coordinate of the vertex. The easiest way is simply to remember that the x-coordinate of the vertex is always equal to -b/2a, where a is the coefficient of the x2 term and b is the coefficient of the x term.
152008
To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x. You can also use the graph of the line to find the x intercept. Just look on the graph for the point where the line crosses the x-axis, which is the horizontal axis. That point is the x intercept.
1338770
Step 2: Use the formula y = mx + b to determine the y-intercept, b. Replace x and y in the formula with the coordinates of one of the given points, and replace m with the calculated value, (2). Find the equation of the line whose graph contains the points (1,–2) and (6,5). The answer will look like y = mx + b.
1435983
Graph B: This parabola's vertex is on the y-axis, so the axis of symmetry is the y-axis. That means that the function is even. Graph C: This cubic is centered on the origin. ... Graph F: This square root has no symmetry.