Q74. - Algebra 1

Question

WRITING MATH Explain how to find the axis of symmetry from an equation for a quadratic equation. What other characteristics of the graph can you derive from the equation? Explain.

Step-by-Step Solution

Answer

To find the axis of symmetry, substitute the values of into $x=-\frac{b}{2a}$. The other characteristics of the graph derivable from the equation are vertex and y-intercept.

Step 1. Axis of symmetry.

Parabola is symmetric about a central line which is known as the axis of symmetry. 

A standard form of a quadratic equation is given by $y=a{x}^2+bx+c$ and the axis of symmetry is given by $x=-\frac{b}{2a}$. To find the axis of symmetry, substitute the values of a,b into $x=-\frac{b}{2a}$.

Step 2. Vertex.

The axis of symmetry that intersects a parabola at only one point is called the vertex. As the axis of symmetry passes through the vertex it has an x-coordinate of the vertex $\left(x,y\right)$ is $x=-\frac{b}{2a}$. Substitute the value of $x=-\frac{b}{2a}$ in the equation and solve for to get the coordinates of the vertex.

Step 3. y-intercept.

y-coordinate of the point at which the graph cuts the y-axis is the y-intercept of the graph. By substituting 0 for x, y-intercept can be found.