Solve Quadratics by Graphing

Front

What are the solutions of a quadratic equation?

Back

The solutions of a quadratic equation are the values of x that make the equation equal to zero, also known as the roots or zeroes.

Front

How do you find the solutions of the quadratic equation y = x^2 + 6x - 7 using graphing?

Back

You can graph the equation using a graphing tool like DESMOS and identify the points where the graph intersects the x-axis. These points are the solutions.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph crosses the x-axis, which correspond to the solutions of the equation.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two equal halves, and it can be found using the formula x = -b/(2a) for the quadratic equation ax^2 + bx + c.

Front

What are the zeroes of the quadratic function?

Back

The zeroes of a quadratic function are the same as the solutions or roots, which are the values of x for which the function equals zero.

Front

How can you determine the vertex of a parabola from its equation?

Back

The vertex of a parabola can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at x = h.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic equation indicate about the parabola?

Back

The coefficient 'a' indicates the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, x-intercepts, and y-intercept, then plot these points and draw a smooth curve.